Question

The measures of the angles of △RST are given by the expressions in the table.

Angle Measure
R 31°
S ​(x+4)∘
T ​(3x+9)∘
Find the value of x. Then find the m∠S and m∠T.



Enter your answers in the boxes.
x =

​ m∠S= ​
4 º

​ m∠T= ​
5 º

Answer 1

Enter your answers in the boxes.
x = 34°

​ m∠S= ​38°


​ m∠T= ​111°
Hope it was helpful

Answer 2

Solution :-

Given = m∠R = 31°

As we know that the sum of all three angles of a triangle equals to 180 degrees.

⇒ m∠R + m∠S + m∠T = 180°

⇒ 31° + (x + 4)° + (3x + 9)° = 180°

⇒ 31 + 4 + 9 + x + 3x = 180

⇒ 44 + 4x = 180

⇒ 4x = 180 - 44

⇒ 4x = 136

⇒ x = 136/4

⇒ x = 34°

m∠S = (x + 4)°

⇒ 34 + 4 = 38°

m∠T = (3x + 9)°

⇒ (3*34) + 9

⇒ 102 + 9 = 111°

So, m∠S = 38° and m∠T = 111°

Answer.