Answer and Step-by-step explanation:
Hello!
To find the angles of this triangle, we would look at the markings and angle measurements that are already on the triangle.
We see on the top triangle that the sides are congruent. That means angle 1 and 2 are the same. To find those angles, we would subtract 55 from 180, then divide by 2.
180 - 55 = 125
125 ÷ 2 = 62.5
Angle 1: 62.5
Angle 2: 62.5
We see angle 3 is opposite of 55. These two angles are congruent by the vertical angles theorem.
Angle 3: 55
On the bottom left of the bottom triangle, we see the angle 105 that is supplementary to the angle 4. These angles are supplementary angles, in which they will add up to 180. To find angle 4, we subtract 105 from 180.
180 - 105 = 75
Angle 4: 75
We know that triangles' angles add up to 180, so to find angle 5, we subtract angle 3 and angle 4 from 180, and we can do this because of the Triangle Angle Sum Theorem.
180 - 55 - 75 = 50
Angle 5: 50
Angle 1: 62.5
Angle 2: 62.5
Angle 3: 55
Angle 4: 75
Angle 5: 50
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