find the measure of the three missing angles in the rhombus below.

Explanation:

Step1: Recall rhombus angle - properties

In a rhombus, opposite angles are equal.

Step2: Find angle (x)

Since the angle opposite to the (70^{\circ}) angle is (x), then (x = 70^{\circ}).

Step3: Use the sum - of - interior angles of a quadrilateral

The sum of the interior angles of a quadrilateral is (360^{\circ}). Let the two equal angles be (y) and (z). We know that (2\times70^{\circ}+y + z=360^{\circ}). Since (y = z) (opposite angles of a rhombus are equal), we can rewrite it as (140^{\circ}+2y = 360^{\circ}).

Step4: Solve for (y) and (z)

First, subtract (140^{\circ}) from both sides of the equation (140^{\circ}+2y = 360^{\circ}): (2y=360^{\circ}- 140^{\circ}=220^{\circ}). Then divide both sides by 2: (y=\frac{220^{\circ}}{2}=110^{\circ}), and since (z = y), (z = 110^{\circ}).

Answer:

(x = 70^{\circ}), (y = 110^{\circ}), (z = 110^{\circ})