Question

Can someone help me?

Answer 1

Answer:

m∠R = 112°

m∠S = 112°

m∠T = 68°

Step-by-step explanation:

Quadrilateral QRST is a cyclic quadrilateral.

A cyclic quadrilateral is a quadrilateral drawn inside a circle where every vertex touches the circumference of the circle.  

The opposite angles in a cyclic quadrilateral sum to 180°.

⇒ m∠Q + m∠S = 180°

⇒ m∠R + m∠T = 180°

Given:

• m∠Q = 68°
• m∠R = (3x + 40)°
• m∠T = (5x - 52)°

Measure of angle Q

⇒ m∠Q + m∠S = 180°

⇒ 68° + m∠S = 180°

⇒ m∠S = 180° - 68°

⇒ m∠S = 112°

Measure of angles R and T

⇒ m∠R + m∠T = 180°

⇒ (3x + 40)° + (5x - 52)° = 180°

⇒ )8x -12)° = 180°

⇒ 8x° = 192°

⇒ x = 24

Substituting the found value of x into the expressions for angles R and T:

⇒ m∠R = (3(24) + 40)°

⇒ m∠R = 112°

⇒ m∠T = (5x - 52)°

⇒ m∠T = 68°