Question

properties of isosceles triangles
score: 0/3 penalty: 1 off
question
in \\( \triangle o p q, \overline{p q} \cong \overline{o p} \\) and \\( \mathrm{m} \angle p=121^{\circ} \\). find \\( \mathrm{m} \angle o \\).
answer attempt 1 out of 2
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Explanation:

Step1: Use the property of isosceles triangle

Since \(\overline{PQ}\cong\overline{OP}\), \(\triangle OPQ\) is isosceles with \(\angle O=\angle Q\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(m\angle O = x\) and \(m\angle Q=x\) (because \(\angle O\cong\angle Q\) in \(\triangle OPQ\) as \(\overline{PQ}\cong\overline{OP}\)), and \(m\angle P = 121^{\circ}\). Then \(x + x+121^{\circ}=180^{\circ}\).

Step3: Solve the equation

Combine like terms: \(2x=180^{\circ}- 121^{\circ}\). So \(2x = 59^{\circ}\), then \(x=\frac{59^{\circ}}{2}=29.5^{\circ}\).

Answer:

\(29.5^{\circ}\)