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wegnerkolmp2741o

Answer:

Q = 82

Step-by-step explanation:

According to the inscribed quadrilateral theorem, the opposite angles of quadrilateral must be supplementary, meaning they add up to 180.

<Q + < S = 180

x+53 + x + 69 = 180

Combine like terms.

2x+122 =180

Subtract 122 from each side.

2x = 180-122

2x = 58

Divide each side by 2.

x= 29

Now find angle Q

Q = x+53

Q = 29+53

Q = 82

Despina

Answer:

  • m∠Q = 82°

Step-by-step explanation:

We know that the Opposite angles in a cyclic quadrilateral should always total 180°.

Here ∠Q and ∠S are the Opposite angles

  • ∠Q + ∠S = 180°
  • x + 53° + x + 69° = 180°
  • 122 + x = 180

subtract 122 from both sides,

  • 2x = 180 - 122
  • 2x = 58°

divide both sides by 2,

  • x = 29

To find m∠Q, substitute the value of (x = 29) in x + 53°

  • m∠Q = x + 53
  • m∠Q = 29 + 53
  • m∠Q = 82°

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