Question

The measures of the angles of △ABC are given by the expressions in the table.
What is the measure of ∠A and ∠C ?

Enter your answers in the boxes.
​ m∠A= ​

​ m∠C= ​

Answer 1

The value of x is 32, m∠A = 115° and m∠C = 50°.

Solution:

Given ABC is a triangle.

m∠A = (4x - 13)°, m∠B = 15° and m∠C = (x + 18)°

Sum of the angles of a triangle = 180°

m∠A + m∠B + m∠C = 180°

⇒ (4x - 13)° + 15° + (x + 18)° = 180°

⇒ 4x° - 13° + 15° + x° + 18° = 180°

⇒ 5x° + 20° = 180°

Subtract 20° from both sides.

⇒ 5x° = 160°

Divide by 5 on both sides.

⇒ x° = 32°

⇒ x = 32

m∠A = (4x - 13)°

        = (4(32) - 13)°

m∠A = 115°

m∠C = (x + 18)°

        = (32 + 18)°

m∠C = 50°

Hence the value of x is 32, m∠A = 115° and m∠C = 50°.