Question

previous answer: 9
what is the measure of ∠q?
there is a trapezoid pqrs, with pq and sr being the two bases (marked with arrows indicating they are parallel). the legs ps and qr are marked as equal (with tick marks). the measure of ∠p is (17x - 45)° and the measure of ∠q is (11x + 9)°.

Explanation:

Step1: Identify supplementary angles

$\angle P + \angle Q = 180^\circ$

Step2: Substitute angle expressions

$(17x - 45) + (11x + 9) = 180$

Step3: Simplify and solve for $x$

$28x - 36 = 180$
$28x = 216$
$x = \frac{216}{28} = \frac{54}{7}$

Step4: Calculate $\angle Q$

$\angle Q = 11\times\frac{54}{7} + 9$

Answer:

$\frac{663}{7}^\circ$ or approximately $94.71^\circ$