Triangle Q S R. Angle Q is 98 degrees and angle R is 37.6 degrees. Triangle T U V. Angle U is 98 degrees and angle V is 37.6 degrees. Answer these questions about finding the missing angle measures. What is the measure of ∠Q? What is the measure of ∠T? What can be concluded about these triangles?

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Mathematics

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11 August, 07:47

Triangle Q S R. Angle Q is 98 degrees and angle R is 37.6 degrees. Triangle T U V. Angle U is 98 degrees and angle V is 37.6 degrees. Answer these questions about finding the missing angle measures. What is the measure of ∠Q? What is the measure of ∠T? What can be concluded about these triangles?

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Answers (1)

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Yasmin Shepherd · Answer 1

The measures of angles are ∠Q=47.4° and ∠T=47.4°.

The triangles are similar, because their corresponding angles have equal measures.

Step-by-step explanation:

The sum of a triangle's angles is always 180 degrees.

First for triangle ΔQSR there is

∠Q=180°-∠S-∠R=180°-37.6°-98°=47.4°,

and for triangle ΔTUV:

∠T=180°-∠U-∠V=180°-37.6°-98°=47.4°.

together ∠Q=47.4° and ∠T=47.4°.

Because ∠Q=∠T, ∠S=∠U and ∠R=∠V (the corresponding angles of two triangles has equal measures), the triangles are similar.