Question

The measures of the angles of △RST are given by the expressions in the table.
Find the value of x. Then find the m∠S and m∠T.

Enter your answers in the boxes.
x =
​ m∠S= ​

Answer 1

The value of x is 34, m∠S = 38° and m∠T = 111°.

Solution:

Given RST is a triangle.

m∠R = 31°, m∠S = (x + 4)° and m∠T = (3x + 9)°

Sum of the angles of a triangle = 180°

m∠R + m∠S + m∠T = 180°

⇒ 31° + (x + 4)° + (3x + 9)° = 180°

⇒ 31° + x° + 4° + 3x° + 9° = 180°

⇒ 44° + 4x° = 180°

Subtract 44° from both sides.

⇒ 4x° = 136°

Divide by 4 on both sides.

⇒ x° = 34°

⇒ x = 34

m∠S = (x + 4)°

        = (34 + 4)°

m∠S = 38°

m∠T = (3x + 9)°

        = (3(34) + 9)°

m∠T = 111°

Hence the value of x is 34, m∠S = 38° and m∠T = 111°.