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= ​__ º


m∠T= ​__ º

Answer 1

interior angles of a triangle add up to 180 degrees

31 + x + 4 + 3x + 9 = 180
44 + 4x = 180
4x = 180 - 44
4x = 136
x = 136/4
x = 34 <===

< R = 31
< S = x + 4.....34 + 4 = 38 <==
< T = 3x + 9.....3(34) + 9 = 111 <==

Answer 2

The measure of angle S is $38^\circ$ and the measure of angle T is $111^\circ$ and this can be determined by using the property of sum of interior angles.

Given :

• $\rm \angle R = 31^\circ$

• $\rm \angle S = (x + 4)^\circ$

• $\rm \angle T = (3x+9)^\circ$

Apply the property of the sum of the interior angles of the triangle in order to determine the angles R, S, and T.

$\rm \rm \angle R +\rm \angle S+\rm \angle T = 180^\circ$

31 + (x + 4) + (3x + 9) = 180

Simplify the above equation in order to determine the value of 'x'.

4x + 13 = 149

4x = 136

$\rm x = 34^\circ$

Now, the measure of angle S is:

$\rm \angle S = x + 4 = 34 + 4 = 38^\circ$

$\rm \angle T = 3x + 9 = 3(34) + 9= 111^\circ$

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https://brainly.com/question/21286835