Question

1. find the measure of each numbered angle in the rhombus shown below.

$m\angle1 = $
$m\angle2 = $
$m\angle3 = $
$m\angle4 = $
$m\angle5 = $

Explanation:

Step1: Find $\angle1$

In a rhombus, opposite angles are equal. $\angle1$ is opposite the given $70^\circ$ angle, so $m\angle1 = 70^\circ$.

Step2: Calculate $\angle2$ and $\angle5$

In a rhombus, consecutive angles are supplementary. First find the adjacent angle to $70^\circ$: $180^\circ - 70^\circ = 110^\circ$. The diagonal bisects this angle, so $m\angle2 = m\angle5 = \frac{180^\circ - 70^\circ}{2} = 40^\circ$.

Step3: Find $\angle3$

In the triangle containing $\angle1$ and $\angle2$, angles sum to $180^\circ$. $m\angle3 = 180^\circ - m\angle1 - m\angle2 = 180^\circ - 70^\circ - 40^\circ = 70^\circ$.

Step4: Find $\angle4$

In a rhombus, opposite angles are equal. $\angle4$ is opposite the given $70^\circ$ angle, so $m\angle4 = 70^\circ$.

Answer:

$m\angle1 = 70^\circ$, $m\angle2 = 40^\circ$, $m\angle3 = 70^\circ$, $m\angle4 = 70^\circ$, $m\angle5 = 40^\circ$