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40 votes
40 votes
1. If PQ || SR and PQRS is an isosceles trapezoid,

find m<1.
A. 30°
B. 32°
C. 34°
D. 36°

1. If PQ || SR and PQRS is an isosceles trapezoid, find m<1. A. 30° B. 32° C. 34° D-example-1
User Bluemarble
by
2.5k points

1 Answer

17 votes
17 votes

Answer:

B. 32°

Explanation:

Finding ∠S and ∠R

  • ∠S = 58°
  • ∠S = ∠R (Isoceles trapezoid)
  • ⇒ ∠R = 58°

Similarly, ∠P = ∠Q (same reason as above)

Applying the Angle Sum Property of Quadrilaterals,

  • ∠P + ∠Q + ∠R + ∠S = 360°
  • 2∠P + 2∠S = 360°
  • ∠P + ∠S = 180°
  • ∠P = 180° - 58°
  • ∠P = 122° = ∠Q

Finding the missing angles of the triangle

  • Left angle : ∠x + 96° = 122°
  • ∠x = 26°

Applying the Angle Sum Property of Triangles,

  • ∠x + ∠Q + ∠1 = 180°
  • 26° + 122° + ∠1 = 180°
  • ∠1 = 180° - 148°
  • ∠1 = 32°
User Batbaatar
by
3.3k points
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