Question

problem solving (lms graded)
due jan 30 - 11:59 pm
writing for the figure shown, find m∠1. use pencil and paper. explain two ways to find the missing angle measure of the triangle.
(the figure is not drawn to scale.)
m∠1 = \\(\square\\)°

Explanation:

Step1: Identify triangle type

The triangle is right - angled, so one angle is \(90^{\circ}\), another is \(34^{\circ}\).

Step2: Method 1 - Triangle angle sum

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle inside the triangle be \(x\). Then \(34^{\circ}+90^{\circ}+x = 180^{\circ}\), so \(x=180^{\circ}-34^{\circ}-90^{\circ}=56^{\circ}\). Then \(\angle1\) and \(x\) are supplementary (linear pair), so \(m\angle1 = 180^{\circ}-56^{\circ}=124^{\circ}\).

Step3: Method 2 - Exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For \(\angle1\), the two non - adjacent interior angles are \(90^{\circ}\) and \(34^{\circ}\). So \(m\angle1=90^{\circ}+34^{\circ}=124^{\circ}\).

Answer:

\(124\)