Question

question
in $\triangle mno$, $overline{om}congoverline{no}$ and $mangle n = 17^{circ}$. find $mangle m$.

Explanation:

Step1: Identify the triangle type

Since \(\overline{OM}\cong\overline{NO}\), \(\triangle MNO\) is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are equal. So \(\angle M=\angle O\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle M = x\) and \(m\angle O=x\) (because \(\angle M\) and \(\angle O\) are equal), and \(m\angle N = 17^{\circ}\). Then \(x + x+17^{\circ}=180^{\circ}\).
Combine like terms: \(2x+17^{\circ}=180^{\circ}\).
Subtract \(17^{\circ}\) from both sides: \(2x=180^{\circ}- 17^{\circ}=163^{\circ}\).
Divide both sides by 2: \(x=\frac{163^{\circ}}{2}=81.5^{\circ}\).

Answer:

\(m\angle M = 81.5^{\circ}\)