Question

The measures of the angles in △ABC are given by the expressions in the table. Angle Measure
A 65°
B (3x−10)°
C (2x)°
Find the value of x. Then find the measures of angles B and C. Enter your answers in the boxes.
x =
m∠B= º
m∠C= ​ º

Answer 1

angles in a triangle add up to 180 degrees

65 + 3x - 10 + 2x = 180
5x + 55 = 180
5x = 180 - 55
5x = 125
x = 125/5
x = 25 <===

m < B = 3x - 10
m < B = 3(25) - 10
m < B = 75 - 10
m < B = 65 <====

m < C = 2x
m < C = 2(25)
m < C = 50 <====

Answer 2

The measures of the angles and x are as follows:

x = 25

∠B = 65°

∠C = 50°

The measure of triangle ABC are as follows:

• ∠A = 65°
• ∠B = (3x - 10)°
• ∠C = (2x)°

Properties of a triangle;

• Sum of it angles equals to 180 degrees

• Triangle has 3 sides and angles.

Therefore,

65 + 3x - 10 + 2x = 180

55 + 5x= 180

5x = 180 - 55

5x = 125

x = 125 / 5

x = 25

Therefore,

∠B = 3(25) - 10 = 65°

∠C = 2(25)  =50°

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