Question

directions: find all missing angles.
1
76°
59°
m∠1 =
2
62°
67°
m∠1 =
3
152°
115°
m∠1 =
4.
5.
this is a 2 - page document

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Solve for \(m\angle1\) in the first triangle

Let the angles of the first triangle be 76°, 59°, and \(\angle1\). Then \(m\angle1=180-(76 + 59)\).
\[m\angle1=180 - 135=45^{\circ}\]

Step3: Solve for \(m\angle1\) in the second triangle

Let the angles of the second triangle be 62°, 67°, and \(\angle1\). Then \(m\angle1=180-(62 + 67)\).
\[m\angle1=180 - 129 = 51^{\circ}\]

Step4: Use the exterior - angle property for the third triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Let the exterior angle be 152° and one non - adjacent interior angle be 115°. Then \(m\angle1=152 - 115=37^{\circ}\)

Answer:

1. \(m\angle1 = 45^{\circ}\)
2. \(m\angle1 = 51^{\circ}\)
3. \(m\angle1 = 37^{\circ}\)