Question

If RS=RU=92, m∠RTS=y+26°, and m∠RTU=2y, what is m∠STU?

Answer 1

• m∠STU = 104°

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Given

• RS = RU = 92,
• m∠RTS = y + 26°,
• m∠RTU = 2y,
• RU ⊥ TU and RS ⊥ TS.

Solution

Right triangles RTU and RTS are congruent according to HL postulate as per given details above.

It makes RTU and RTS angles congruent as corresponding angles of congruent triangles:

• m∠RTS = m∠RTU
• y + 26 = 2y
• 2y - y = 26
• y = 26

Find the value of angle STU:

• m∠STU = 2*m∠RTU = 2*2*26 = 104