Question

Given: ΔSTQ, ST = TQ

Line SD is perpendicular to TQ
m∠1=32°
Find: m∠S, m∠T, m∠Q

Answer 1

s=58 degrees, Q=58 degrees, T=64 degrees

Step-by-step explanation:

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

Answer 2

Answer: m∠S = 58 ° ; m∠T = 64 ° ; m∠Q = 58 ° .
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Step-by-step 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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