Question

in $\triangle mno$, $overline{mn}congoverline{om}$ and $mangle o = 33^{circ}$. find $mangle m$.

Explanation:

Step1: Use the property of isosceles triangle

Since \(\overline{MN}\cong\overline{OM}\), \(\triangle MNO\) is isosceles with \(\angle N=\angle O\). Given \(m\angle O = 33^{\circ}\), so \(m\angle N=33^{\circ}\).

Step2: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle M=x\). Then \(x + m\angle N+m\angle O=180^{\circ}\). Substitute \(m\angle N = 33^{\circ}\) and \(m\angle O = 33^{\circ}\) into the equation: \(x+33^{\circ}+33^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Simplify the left - hand side of the equation: \(x + 66^{\circ}=180^{\circ}\). Subtract \(66^{\circ}\) from both sides: \(x=180^{\circ}-66^{\circ}\).

Answer:

\(114^{\circ}\)