Question

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Answer 1

Answer:Angle x=70°

Step-by-step explanation:interior angles add up to 180° so we add 41° and 69°. After addition,you minus from 180° and you get 70°

Answer 2

Answer:

• X = 70°
• arc ZY = 140°
• arc XY = 82°

Step-by-step explanation:

The angle sum theorem helps you compute the angle inside the triangle. The inscribed angle theorem helps you compute the arc measures outside the triangle.

Theorems

The Angle Sum theorem tells you the sum of angles in a triangle is 180°. That lets you write the equation ...

  X +Y +Z = 180°

  X +69° +41° = 180°

The Inscribed Angle theorem tells you an inscribed angle has half the measure of the central angle subtending the same arc. The arc and the central angle have the same measure: twice that of the inscribed angle.

  arc ZY = 2×∠X

  arc XY = 2×∠Z

Solutions

Using the equations we wrote describing the relationships of the unknowns to the known information, we find ...

  X = 180° -110° = 70°

  arc ZY = 2×70° = 140°

  arc XY = 2×41° = 82°