Question

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

Explanation:

Step1: Recall property of cyclic quadrilateral

Opposite angles of a cyclic quadrilateral are supplementary. So, $\angle RST+\angle TQR = 180^{\circ}$.

Step2: Set up the equation

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

Step3: Combine like - terms

$5x+4x+15 + 3=180$, which simplifies to $9x+18 = 180$.

Step4: Solve for $x$

Subtract 18 from both sides: $9x=180 - 18=162$. Then divide both sides by 9: $x=\frac{162}{9}=18$.

Step5: Find the measure of $\angle RST$

Substitute $x = 18$ into the expression for $\angle RST$: $\angle RST=5x + 15=5\times18+15=90 + 15=105^{\circ}$.

Answer:

$105^{\circ}$