Question 148651: AH! I need help!
In the convex quadrilateral ABCD if ,angel a is congruent to angel d and, measure of angel b=110 degrees and measure of c=60 find a .
a.95 °
b.170°
c.190°
d.360°
Suppose that the interior angles of a convex pentagon are five consecutive numbers. What is the measure of the largest angle?
a.105°
b.106°
c.109°
d.110°
If the exterior angles of a convex octagon are , and , calculate the smallest of the eight angles.
a.19°
b.21°
c.32°
d.37°
If five of the exterior angles of a convex hexagon measure 55°, 60°, 63°, 70°, and 81°, find the measure of the sixth exterior angle.
a.31°
b.60°
c.120°
d.391°
If the exterior angles of a convex octagon are , and , calculate the smallest of the eight angles.
a.19°
b.21°
c.32°
d.37°
How many sides would a regular polygon have if each interior angle measures 162°?
a.10
b.12
c.18
d.20
How many angles would a regular polygon have if each exterior angle measures 5°?
a.36
b.37
c.72
d.74
Answer by mangopeeler07(462)   (Show Source):
You can put this solution on YOUR website! 1. In the convex quadrilateral ABCD if ,angel a is congruent to angel d and, measure of angel b=110 degrees and measure of c=60 find a .
a.95 °
b.170°
c.190°
d.360°
add b and c: 110 +60=170
subtract that from 360, since the degrees of a quad is 360:
360-170=190
Divide that by two since a and d are congruent
190/2=95
So the answer is a)95 degrees.
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2. Suppose that the interior angles of a convex pentagon are five consecutive numbers. What is the measure of the largest angle?
a.105°
b.106°
c.109°
d.110°
Since these five numbers are consecutive, then this can be written as:
x+(x+1)+(x+2)+(x+3)+(x+4)
Set that equal to 540, since the angles of pentagon add up to 540:
x+(x+1)+(x+2)+(x+3)+(x+4)=540
Combine like terms:
5x+10=540
5x=530
x=106
Largest angle=x+4 or 106+4
Largest angle=110 degrees
So the answer is d)110 degrees.
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3. If five of the exterior angles of a convex hexagon measure 55°, 60°, 63°, 70°, and 81°, find the measure of the sixth exterior angle.
a.31°
b.60°
c.120°
d.391°
First find the measure of the first five interior angles, which can be found by subtracting the exterior angle from 180. You get:
125, 120, 117, 110, and 99.
Now add them together:
125+120+117+110+99=571
Now subtract that from 720, since the degrees of a hexagon add up to 720.
720-571=149
That is the sixth interior angle. Now subtract that from 180 to get the exterior:
180-149=31
So the answer is a)31 degrees.
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4. How many sides would a regular polygon have if each interior angle measures 162°?
a.10
b.12
c.18
d.20
Use the formula [180(n-2)]/n to get the measure of an interior angle of a regular polygon. If each angle is 162, then set it equal to that:
[180(n-2)]/n=162
Now multiply both sides by n
180(n-2)=162n
Distribute 180 to n-2
180n-360=162n
Subtract 180n from both sides
-360=-18n
Divide both sides by -18
20=n
So the answer is d)20 sides.
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5. How many angles would a regular polygon have if each exterior angle measures 5°?
a.36
b.37
c.72
d.74
First get the measure of the interiors by subtracting the exterior from 180:
180-5=175.
Then use [180(n-2)]/n as in the last question, but this time set it equal to 175:
[180(n-2)]/n=175
Now multiply both sides by n
180(n-2)=175n
Distribute 180 to n-2
180n-360=175n
Subtract 180n from both sides
-360=-5n
Divide both sides by -5
72=n
So the answer is c)72 angles.
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