Question

your uncle bob is a bricklayer who was given the job of building a brick wall around a garden that is shaped like a regular triangle. use the linear pairs theorem to calculate the measures of the interior angles.

$m\angle1 =$

$m\angle2 =$

$m\angle3 =$

Explanation:

Step1: Recall the Linear Pairs Theorem

The Linear Pairs Theorem states that if two angles form a linear pair, then they are supplementary (their sum is \(180^{\circ}\)). A regular triangle has all exterior angles equal. The sum of an exterior angle and its adjacent interior angle is \(180^{\circ}\). Also, the sum of exterior angles of any polygon is \(360^{\circ}\). For a triangle (3 - sided polygon), each exterior angle \(e=\frac{360^{\circ}}{3}=120^{\circ}\).

Step2: Calculate the interior angles

Let the interior angle be \(i\). Using the linear - pair relationship \(i + e=180^{\circ}\). Substitute \(e = 120^{\circ}\) into the equation: \(i=180^{\circ}-e\). So \(i = 180^{\circ}-120^{\circ}=60^{\circ}\). Since the triangle is regular (equilateral), all interior angles are equal.

Answer:

\(m\angle1 = 60^{\circ}\), \(m\angle2=60^{\circ}\), \(m\angle3 = 60^{\circ}\)