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17 November, 20:14

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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  1. 17 November, 20:23
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    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.
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