Question

in quadrilateral qrst, ∠rst measures (5x+15)°. angle tqr measures (4x+3)°. what is the measure of angle rst? 15° 75° 105° 165°

Explanation:

Step1: Recognize cyclic quadrilateral rule

In a cyclic quadrilateral, opposite angles sum to $180^\circ$. So $\angle RST + \angle TQR = 180^\circ$.

Step2: Substitute angle expressions

$(5x+15) + (4x+3) = 180$

Step3: Simplify and solve for x

Combine like terms: $9x + 18 = 180$
Subtract 18: $9x = 162$
Divide by 9: $x = 18$

Step4: Calculate $\angle RST$

Substitute $x=18$ into $5x+15$: $5(18)+15 = 90+15$

Answer:

105°