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Answer:
m∠STU = 42°
Explanation:
We need a relation between angle RTS and angle RTU. We are told that RS is congruent to RU, and we know RT is congruent to itself, so we can claim right triangles RUT and RST are congruent by the HL postulate.
Corresponding angles in congruent triangles are congruent. This means ...
angle RTS = angle RTU
5w -69° = w +3°
4w = 72° . . . . . . . . . add 69°-w to both sides
w = 18°
Then angle RTU is w+3° = 18° +3° = 21°. The angle we're to find is angle STU, which is double this measure: angle STU = angle RTS + angle RTU = 21° +21°.
m∠STU = 42°