Question

find the measure of each numbered angle.
m∠1 = , m∠2 = , m∠3 =
need help?

Explanation:

Step1: Calculate $\angle1$

Sum of angles in $\triangle UTV$: $180^\circ - 35^\circ - 36^\circ = 109^\circ$. $\angle1$ is supplementary to this: $180^\circ - 109^\circ = 71^\circ$.

Step2: Calculate $\angle2$

Sum of angles in $\triangle RUV$: $180^\circ - 80^\circ - 35^\circ = 65^\circ$. So $\angle2 = 65^\circ$.

Step3: Calculate $\angle3$

$\angle3$ is vertical to $\angle1$: $\angle3 = \angle1 = 71^\circ$.

Answer:

$m\angle1 = 71^\circ$, $m\angle2 = 65^\circ$, $m\angle3 = 71^\circ$