Question

determine the unknown interior angle measure(s) in each triangle

∠zxy = ______

∠edf = ______

∠jkl = ______

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Calculate $\angle ZXY$

For the first triangle with angles 65° and 40°, let $\angle ZXY=x$. Then $x + 65^{\circ}+40^{\circ}=180^{\circ}$, so $x=180^{\circ}-(65^{\circ} + 40^{\circ})=180^{\circ}-105^{\circ}=75^{\circ}$.

Step3: Calculate $\angle EDF$

For the second triangle with angles 86° and 63°, let $\angle EDF = y$. Then $y+86^{\circ}+63^{\circ}=180^{\circ}$, so $y = 180^{\circ}-(86^{\circ}+63^{\circ})=180^{\circ}-149^{\circ}=31^{\circ}$.

Step4: Calculate $\angle JKL$

For the third triangle with angles 21° and 18°, let $\angle JKL = z$. Then $z+21^{\circ}+18^{\circ}=180^{\circ}$, so $z=180^{\circ}-(21^{\circ}+18^{\circ})=180^{\circ}-39^{\circ}=141^{\circ}$.

Answer:

$\angle ZXY = 75^{\circ}$
$\angle EDF = 31^{\circ}$
$\angle JKL = 141^{\circ}$