Answer :
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
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°