Question

in quadrilateral qrst, $\angle rst$ measures $(5x + 15)^{circ}$. angle tqr measures $(4x + 3)^{circ}$.
what is the measure of angle rst?
$\bigcirc$ $15^{circ}$
$\bigcirc$ $75^{circ}$
$\bigcirc$ $105^{circ}$
$\bigcirc$ $165^{circ}$

Explanation:

Step1: Use cyclic quadrilateral property

Opposite angles sum to $180^\circ$:
$(5x+15)^\circ + (4x+3)^\circ = 180^\circ$

Step2: Simplify and solve for $x$

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

Step3: Calculate $\angle RST$

Substitute $x=18$ into $(5x+15)^\circ$:
$5(18) + 15 = 90 + 15 = 105$

Answer:

105°