Question

for the figure shown on the right, find m∠3 and m∠4. m∠3 = □°

Explanation:

Step1: Use angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. In the given triangle, if we consider the three interior angles, we can find $\angle4$. Let the third interior angle of the triangle be $x$. So, $x + 41^{\circ}+40^{\circ}=180^{\circ}$. Then $x = 180^{\circ}-(41^{\circ}+40^{\circ})=99^{\circ}$. And $\angle4$ and $x$ are vertical angles, so $\angle4=x = 99^{\circ}$.

Step2: Use linear - pair property

$\angle3$ and $\angle4$ form a linear - pair. A linear - pair of angles is supplementary, i.e., $\angle3+\angle4 = 180^{\circ}$. Since $\angle4 = 99^{\circ}$, then $\angle3=180^{\circ}-\angle4=180^{\circ}-99^{\circ}=81^{\circ}$.

Answer:

$m\angle3 = 81^{\circ}$, $m\angle4 = 99^{\circ}$