Respuesta :
Answer:
Fourth option is correct m Angle P Q R = 96 and m Angle P S R = 84
Therefore,
[tex]m\angle PQR =96\°\\\\m\angle PSR = 84\°[/tex]
Step-by-step explanation:
Given:
In quadrilateral PQRS,
∠PQR = (7x - 2)°
∠PSR = (5x + 14)°
Circle T is inscribed with quadrilateral P Q R S.
To Find:
m∠PQR = ?
m∠PSR = ?
Solution:
Circle T is inscribed with quadrilateral P Q R S.
Therefore,
Quadrilateral PQRS is a Cyclic Quadrilateral,
So for a Cyclic Quadrilateral, opposite Angles are Supplementary
∠PQR and ∠PSR are opposite angles
∴ [tex]m\angle PQR+ m\angle PSR =180\°[/tex]
Substituting the values we get
[tex](7x-2)+(5x+14)=180\\\\12x+12=180\\\\12x=180-12=168\\\\x=\dfrac{168}{12}=14[/tex]
Substitute x in PQR and PSR we get
[tex]m\angle PQR = 7\times 14 - 2 =96\°\\\\m\angle PSR = 5\times 14 + 14=84\°[/tex]
Therefore,
[tex]m\angle PQR =96\°\\\\m\angle PSR = 84\°[/tex]
Answer:
m Angle P Q R = 96o and m Angle P S R = 84o
Step-by-step explanation:
This is the answer 2021 Edge
Hope this Helps!!!!!
