Question

find the measure of each of the numbered angles. if necessary, state your solution as an improper fraction. m∠1 = m∠2 = m∠3 = m∠4 = m∠5 = m∠6 =

Explanation:

Step1: Find $\angle1$

In the left - hand right - triangle, one angle is $40^{\circ}$ and another is $90^{\circ}$. Using the angle - sum property of a triangle ($180^{\circ}$ in a triangle), $m\angle1=180^{\circ}-(90^{\circ} + 40^{\circ})=50^{\circ}$.

Step2: Find $\angle2$

$\angle1$ and $\angle2$ are vertical angles. Vertical angles are equal. So $m\angle2 = m\angle1=50^{\circ}$.

Step3: Find $\angle3$

In the right - hand right - triangle, one non - right angle is $20^{\circ}$. Using the angle - sum property of a triangle, $m\angle3=180^{\circ}-(90^{\circ}+20^{\circ}) = 70^{\circ}$.

Step4: Find $\angle4$

$\angle3$ and $\angle4$ are vertical angles. So $m\angle4=m\angle3 = 70^{\circ}$.

Step5: Find $\angle5$

In the large triangle on the right, we know two angles: one is $m\angle2 = 50^{\circ}$ and another is $m\angle3=70^{\circ}$. Using the angle - sum property of a triangle, $m\angle5=180^{\circ}-(50^{\circ}+70^{\circ})=60^{\circ}$.

Step6: Find $\angle6$

In the left - hand right - triangle, $m\angle6=180^{\circ}-(90^{\circ}+40^{\circ}) = 50^{\circ}$.

Answer:

$m\angle1 = 50$
$m\angle2 = 50$
$m\angle3 = 70$
$m\angle4 = 70$
$m\angle5 = 60$
$m\angle6 = 50$