The missing angles in the triangle is as follows:
- ∠1 = 62.5°
- ∠2 = 62.5°
- ∠3 = 55°
- ∠4 = 75°
- ∠5 = 50°
<h3>How to find the measure of angles in a triangle?</h3>
A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
∠3 = 55 degrees (vertically opposite angles)
Vertically opposite angles are congruent to each other.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Using exterior angle theorem ,
105 = ∠5 + 55
∠5 = 105 - 55
∠5 = 50 degrees
∠4 = 180 - 50 - 55
∠4 = 75 degrees
Therefore, the other triangle is an isosceles triangle. This means the base angles are equal.
Hence,
∠1 = ∠2 = x
2x + 55 = 180
2x = 180 - 55
2x = 125
x = 125 / 2
x = 62.5 degrees.
Hence,
∠1 = ∠2 = 62.5 degrees.
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