Question

find m∠qrs.
answer
attempt 1 out of 2
m∠qrs =
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Explanation:

Step1: Identify the triangle type

Since two sides of the triangle are marked as equal, it is an isosceles triangle. In an isosceles triangle, the base angles are equal. So, \(m\angle Q=m\angle S = 48^{\circ}\).

Step2: Use the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle QRS=x\). Then, using the formula \(m\angle Q + m\angle S+m\angle QRS=180^{\circ}\), we substitute the known values: \(48^{\circ}+48^{\circ}+x = 180^{\circ}\).

Step3: Solve for \(x\)

First, simplify the left - hand side: \(96^{\circ}+x=180^{\circ}\). Then, subtract \(96^{\circ}\) from both sides: \(x=180^{\circ}-96^{\circ}\).

Answer:

\(84\)