Questions: Find m angle TSR

Find m angle TSR
Transcript text: Find $m \angle T S R$
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Solution

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Solution Steps

Step 1: Find the value of x

The sum of the angles in a triangle is 180°. In triangle STU, we have:

m∠SUT + m∠STU + m∠TSU = 180°
m∠SUT + 105° + (2x + 3) = 180°
m∠SUT + 2x + 108 = 180°
m∠SUT + 2x = 72°

Since RSTU is a parallelogram, the sum of adjacent angles is 180°. Therefore,

m∠TSR + m∠TSU = 180
(6x - 8) + m∠TSU = 180
m∠TSU = 180 - (6x -8)
m∠TSU = 188 - 6x

Substitute the value of m∠TSU into the previous equation:

m∠SUT + 2x = 72
m∠SUT = 72 - 2x

Since RSTU is a parallelogram, opposite angles are equal. Therefore,

m∠SUT = m∠TSR
72 - 2x = 6x - 8
80 = 8x
x = 10
Step 2: Find m∠TSR

Substitute the value of x into the expression for m∠TSR:

m∠TSR = 6x - 8
m∠TSR = 6(10) - 8
m∠TSR = 60 - 8
m∠TSR = 52°

Final Answer: The measure of angle TSR is 52°.

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