Questions on Geometry: Angles, complementary, supplementary angles answered by real tutors!

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x+2x+3=90
3x=87
x=29
2x+3=61

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Reread your question...you stated that the measure of D is 45, and you asked for the measure of D.

You probably want the measure of C, which is 180-45 or 135.

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Let represent the measure of the first angle. Then the measure of the second angle must be and the measure of the third angle must be . The sum of the measures of the interior angles of any triangle is , so:



Solve for , then calculate and

John

My calculator said it, I believe it, that settles it

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90 - 64 = 26 degrees

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The complement of an angle is the measure of the angle that must be added to the given angle so that the total of the two measures is 90 degrees.
.
You are given an angle whose measure is 23 degrees. What is the measure of the angle that must be added to make the total equal 90 degrees? You can find that angle by subtracting 23 degrees from 90 degrees. That subtraction results in:
.
90 - 23 = 67
.
So the complement of an angle whose measure is 23 degrees is an angle whose measure is 67 degrees.
.
I hope this helps you to understand the concept of complementary angles. Complementary angles are two angles whose measures add up to 90 degrees.
.

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If m angle 2= 42 degrees, what does m angle 1 equal?
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Not enough info.

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2 X 7 = 14 or
1 X 14 = 14

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Add 147°41'28" + 27°20'21"

[Note: to make a degree symbol °, be sure NumLock is on and lit.  Hold down
the Alt key with your left hand while typing 248 on the number key-pad
way on the far right side of your keyboard.  When you let up the Alt key
the ° will magically appear on the screen.  Don't use the number keys
above the number keys.  They won't work.  You have to use the number keys
on the far right side of the keyboard.]  

 147°41'28" 
+ 27°20'21"
 174°61'49"

Since the number of minutes is 60 or more, we borrow 60' from
the 61 minutes, leaving it with 1', change the 60' we borrowed
to 1° and add it to the degrees, making it 175°. so we have:

 147°41'28" 
+ 27°20'21"
 174°61'49"
 175° 1'49"

Express 142.04° without a decimal

Write down the whole part of 142.04, which is 142 followed by 
a degree symbol "°":

142°

Multiply the decimal part of 142.04, which is .04, by 60, 
getting 2.4. Beside the degree symbol write down that whole part 
of 2.4, which is 2 followed by a minute symbol "'".  So far you 
have:

142°2'

Multiply the decimal part of 2.4, which is .4, by 60, 
getting 24. Beside the minute mark write down 24 
followed by a second symbol """.  So you end up with

142°2'24"

Edwin

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Each hour mark on the clock is of
a degree circle apart. That is degrees
At 7 pm, the minute hand and hour hand are
degrees apart
The minute hand is moving at the rate of degrees/min
The hour hand is moving at the rate of degree/min
------------------
Let = the degrees that the minute hand travels until it makes
an angle of degrees with the hour hand
Let = the degrees that the hour hand travels until it makes
an angle of degrees with the minute hand
Let = time in minutes until they are degrees apart
------------------
(1)
(2)
(3)
------------------
This is 3 equations and 3 unknowns, so it's solvable
Substitute (2) and (3) into (1)
(1)
(1)
(1)
(1)
(1) min
sec
The hands will be 90 degrees apart at 21 min and 49 sec past 7 PM
hope I got it

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The complement of angle A = 90 - A
The supplement of angle A = 180 - A
Given: 26 times the complement = 11 times the supplement:
26(90-A) = 11(180-A)
(26/11)*90 - (26/11)A = 180 - A
(26/11 - 1)A = 90(26/11 - 2)
15/11A = (4/11)90
A = (4/15)90 = 4*6 = 24

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Given angle: x = 32

Complement: 90 - x = 90 - 32 = 58

Supplement: 180 - x = 180 - 32 = 148

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Presuming that the variable represents a positive value, then all you can say is that the difference between the largest and smallest is:



Had you specified that the figure was a triangle, then I could have been more specific, but since you gave no clue as to how these angles are related I can't go any further.

John

My calculator said it, I believe it, that settles it

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The first sentence in this problem just states the definition of complementary angles. Translation: complementary angles are two angles whose measures add up to be 90 degrees.
.
Then you are told "one angle ...". Stop here and ask yourself, "What is the value of that one angle?" The problem doesn't tell you a value for the measure of that one angle, so it is unknown to you. Let's just call that unknown measure X and it becomes something that you need to solve for.
.
Next you are told "one angle is 21 degrees more than twice the measure of the other." Well, we've called one angle X, so this second angle is 21 degrees more than twice the measure of X. Twice the measure of X is 2 times X or 2X. And 21 degrees more than that means add 21 to 2X to get 2X + 21 as the measure of the second angle.
.
So our 2 angles are X and 2X + 21. Since they are complementary angles we know that when you add the measures of these two angles the sum is 90 degrees. Let's add the measures together and set that equal to 90 as follows:
.
X + 2X + 21 = 90
.
Combine the X and 2X to get 3X and the equation then becomes:
.
3X + 21 = 90
.
Get rid of the 21 on the left side by subtracting 21 from both sides to get:
.
3X = 90 - 21
.
Doing the subtraction on the right side results in the equation becoming:
.
3X = 69
.
Now you can solve for X by dividing both sides by 3 (which is the multiplier of the X) to get:
.
X = 69/3 = 23
.
So we have now found the measure of one of the angles to be 23 degrees. That means that to find the measure of the other angle you can ask yourself how many degrees must its measure be so that when you add it to 23 degrees, the sum will be 90 degrees. You can get that by simply subtracting 23 from 90 to find that the measure of the second angle must be 67 degrees.
.
Just as an added check, let's make sure that when you double the first angle that we found (23 degrees) and add 21 degrees from that, you also get 67 degrees that way. So double 23 degrees to get 46 degrees and add 21 to that and you do, in fact, get 67 degrees. It checks that way also.
.
So the answer is that the measures of the two angles are 23 and 67 degrees.
.
Don't let word problems confuse you too much. Just start by asking yourself "What is the unknown that I need to solve for?" Try to identify that unknown and call it X or something similar. Then try to identify how that unknown relates to the other information in the problem. In this problem the 2X + 21 was one piece of information you were given and the fact that the sum of the two angles needed to be 90 degrees was the other. From those we got the equation that allowed us to solve for X, and once you had X, you could solve for the measure of the other angle.
.
Hope this helps you to understand this problem a little better. Keep trying. You'll eventually get the idea of how to break down word problems into small chunks that you can work with to solve them. Just takes time and patience and practice.
.

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The sum of complementary angles is 90 degrees.
True
False
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It's a fact.
---
For example, 22 & 68 are complementary.

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Let represent the measure of the first angle. Then the measure of the second angle must be and the measure of the third angle must be .

Since the sum of the measures of the interior angles of any triangle is , we can say:



Solve for , then calculate and

John

My calculator said it, I believe it, that settles it