Question

angles p and q are interior angles of an obtuse isosceles triangle. - angle p is obtuse. - angle q is acute. - x represents the measure, in degrees, of angle q. which expression represents the measure, in degrees, of angle p? a 180 - x b 180 - 2x c 90 - x d 90 - 2x

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles in a triangle is $180^\circ$.

Step2: Identify equal angles

The triangle is isosceles, and the obtuse angle is $P$, so the two acute angles are equal: both are angle $Q$ (measure $x$).

Step3: Calculate angle $P$

Subtract the sum of the two acute angles from $180^\circ$.
$180^\circ - (x + x) = 180 - 2x$

Answer:

B. $180 - 2x$