Question

find the measures of angles 1, 2, and 3. (hint: find m∠1, then m∠2, and then m∠3.) the measure of angle 1 is □°. (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Use angle - sum property of a triangle

In the left - hand small triangle, the sum of interior angles of a triangle is 180°. Given two angles 45° and 70°. Let \(m\angle1\) be the third angle. So, \(m\angle1=180-(45 + 70)\).
\[m\angle1=180 - 115=65^{\circ}\]

Step2: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary angles (a linear pair). So, \(m\angle2 = 180 - m\angle1\). Substituting \(m\angle1 = 65^{\circ}\), we get \(m\angle2=180 - 65=115^{\circ}\).

Step3: Find \(m\angle3\)

In the right - hand triangle, one angle is 45° and another is \(\angle2 = 115^{\circ}\). Using the angle - sum property of a triangle (\(180^{\circ}\) for the sum of interior angles), let \(m\angle3\) be the third angle. Then \(m\angle3=180-(45 + 115)\).
\[m\angle3=180 - 160 = 20^{\circ}\]

Answer:

The measure of angle 1 is \(65^{\circ}\), the measure of angle 2 is \(115^{\circ}\), the measure of angle 3 is \(20^{\circ}\)