Question

properties of isosceles triangles (diagram)
question
find m∠mon.
answer
attempt 2 out of 2
m∠mon = °

Explanation:

Step1: Recall angle - sum property of triangle

The sum of interior angles of a triangle is $180^{\circ}$. In $\triangle MON$, we know one angle $\angle MNO = 121^{\circ}$, and since $MN = NO$ (the equal - side markings on the triangle), $\angle NMO=\angle MON$. Let $\angle MON = x$.

Step2: Set up an equation

We have the equation $x + x+121^{\circ}=180^{\circ}$ (because $\angle MNO+\angle NMO+\angle MON = 180^{\circ}$ and $\angle NMO=\angle MON$). Combining like terms gives $2x+121^{\circ}=180^{\circ}$.

Step3: Solve for $x$

Subtract $121^{\circ}$ from both sides: $2x=180^{\circ}- 121^{\circ}=59^{\circ}$. Then divide both sides by 2: $x=\frac{59^{\circ}}{2}=29.5^{\circ}$.

Answer:

$29.5$