Question

Find the measure of

Answer 1

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°

Answer 2

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°