Answer: m∠S = 58 ° ; m∠T = 64 ° ; m∠Q = 58 ° .
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Explanation:
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To find "m∠Q" :
Consider the triangle formed by ∠D , ∠1, and ∠Q ;
Given m∠1 = 32° ;
and m∠D = 90° (a "right triangle" ; as shown in "image attached" ;
and by definition, all triangles have 3 angles and 3 sides; and all 3 angles of a triangle add up to 180° ;
→ m∠Q = 180 − (90 + 32) = 180 − 122 = 58 ;
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Since this is an "isosceles triangle" ;
→ m∠S = m∠Q = 58° .
Since all angles of any triangle add up to " 180° " ;
→ m∠T = 180 − (58 + 58) = 180 − 116 = 64 ;
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Answer: m∠S = 58 ° ; m∠T = 64 ° ; m∠Q = 58 ° .
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