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Find the measure of

Find the measure of-example-1

2 Answers

2 votes

Answer:

See below ~

Explanation:

The total internal measure is 360°.

  • 154° + 60° + 86 + ∠STP + ∠TUP = 360°
  • 2∠STP + 300 = 360°
  • 2∠STP = 60°
  • ∠STP = ∠TUP = 30°

Finding ∠SPQ (clockwise):

  • 2∠STP + 86°
  • 2(30) + 86
  • 146°

Finding ∠SPQ (counterclockwise) :

  • 360° - 146°
  • 214°
User Rushabh Mehta
by
8.0k points
3 votes

Answer:

Angles around a point sum to 360°

⇒ ∠SPT + ∠TPU + 86° + 60° + 154° = 360°

⇒ ∠SPT + ∠TPU = 60°

Therefore:

∠SPQ clockwise = ∠SPT + ∠TPU + 86°

= 60° + 86°

= 146°

∠SPQ anticlockwise = 60° + 154°

= 214°

User Schillingt
by
9.1k points

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