SOLUTION: One angle of a triangle is 3 less than twice another. The other is 4X the sum of the small angle and 2. What are the angle measurements??

Question 211837: One angle of a triangle is 3 less than twice another. The other is 4X the sum of the small angle and 2. What are the angle measurements??
Found 3 solutions by RAY100, tutor_paul, MathTherapy:
Answer by RAY100(1637)   (Show Source): You can put this solution on YOUR website!
sum of the angles of a triangle = 180
.
(x) + (2x-3) + 4(x+2) = 180
.
7x +5 = 180
.
x= 25
.
angles are 25, 47, 108
.

Answer by tutor_paul(519)   (Show Source): You can put this solution on YOUR website!
Let the 3 angles of the triangle be A,B,C.
You know that since it is a triangle, you can write:
Equation #1:
You are given the following information:
Equation #2:
Equation #3:
---------------
You have 3 equations and 3 unknowns. Anytime you have at least as many equations as unknowns, you can solve the problem!
Substitute the expression for C from Equation #3 into Equation #1:

Solve for B in terms of A:

Equation #4:
Substitute Equation #4 into Equation #2:

Solve for A:

Plug this value for A into Equation #2 and solve for B:

Plug the value for A into Equation #3 and solve for C:

Plug these values for A, B, and C into Equation #1 and make sure it still holds true. I will leave that part to you.
==========================
Good Luck,
tutor_paul@yahoo.com

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
One angle of a triangle is 3 less than twice another. The other is 4X the sum of the small angle and 2. What are the angle measurements??

Let the smallest angle be S

Since the middle angle is 3 less than twice the smallest, then middle angle = 2S - 3

Since the largest angle is 4 times the sum of the smallest angle, and 2, then largest angle = 4(S + 2), or 4S + 8

Since the angles of a triangle are supplementary, it follows that:

S + 2S - 3 + 4S + 8 = 180

7S + 5 = 180

7S = 175

= 25

Middle angle = 47 ------> [2(25) - 3]

Largest angle = 108 -----> [4(25 + 2)]

Therefore, the smallest, middle, and largest angles are: , respectively.

RELATED QUESTIONS
One acute angle of a right triangle is not less than 30� more than twice the other acute... (answered by Theo,MathTherapy)
one angle of a triangle is 20 degrees more than the smallest angle. another angle is 8... (answered by josmiceli)
In a triangle, the measure of one angle is twice the measure of another angle. The third... (answered by ewatrrr)
Question 547825: one angle of a triangle is 20 degrees more than the smallest angle.... (answered by solver91311)
The measure of one angle of a triangle is 26 degrees less than twice the measure of... (answered by rm29924)
In a triangle, one angle is 40 more than the smallest and and the 3rd angle is twice the... (answered by harpazo)
In a right triangle, the measure of one acute angle is 30 less than twice the measure of... (answered by stanbon)
One angle of a triangle is 3 times as large as another. The third angle is twice the sum... (answered by mangopeeler07)
one angle of a triangle is 3 times as large as another the third angle is twice the sum... (answered by Alan3354)