Question

1. make sense and persevere is there enough information to determine the measures of the interior angles of the polygon shown? if so, find the measures. if not, explain.

Explanation:

Step1: Identify the polygon type

The figure is a hexagon (6 - sided polygon). The formula for the sum of interior angles of a polygon is $S=(n - 2)\times180^{\circ}$, where $n$ is the number of sides. For $n = 6$, $S=(6 - 2)\times180^{\circ}=720^{\circ}$.

Step2: Analyze given angles

From the diagram, two angles are right angles ($90^{\circ}$ each), and the other four angles seem to be equal (since the hexagon looks symmetric). Let the measure of each of the four equal angles be $x$.

Step3: Set up the equation

The sum of all interior angles is $2\times90^{\circ}+4x = 720^{\circ}$.

Step4: Solve for $x$

Simplify the left - hand side: $180^{\circ}+4x = 720^{\circ}$. Subtract $180^{\circ}$ from both sides: $4x=720^{\circ}- 180^{\circ}=540^{\circ}$. Then divide both sides by 4: $x=\frac{540^{\circ}}{4} = 135^{\circ}$.

Answer:

The two right angles measure $90^{\circ}$ each, and the other four angles measure $135^{\circ}$ each. The sum of interior angles is $720^{\circ}$.