Question

what is the value of p?
triangle rst with s at the bottom left, r at the top, t at the bottom right. sides sr and st are marked as equal (isosceles triangle). angle at s is 30 degrees. angle at t is labeled p.
p = \boxed{\space} degrees

Explanation:

Step1: Identify triangle type

Triangle \(SRT\) is isosceles, since \(SR = ST\) (marked congruent sides).

Step2: Define base angles

In isosceles \(\triangle SRT\), \(\angle R = \angle T = p\).

Step3: Use angle sum property

Sum of angles in a triangle is \(180^\circ\).
$$30^\circ + p + p = 180^\circ$$

Step4: Solve for \(p\)

Simplify and isolate \(p\):
$$2p = 180^\circ - 30^\circ = 150^\circ$$
$$p = \frac{150^\circ}{2} = 75^\circ$$

Answer:

\(75\)