Question

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:

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