Question

Which theorems or postulates could you use to find the measure of angle 1 in the previous question? (2 points)

Same-Side Interior Angles Theorem
Vertical Angles Theorem
Triangle Angle-Sum Theorem
Triangle Exterior Angle Theorem
Alternate Exterior Angles Theorem

Answer 1

I believe that this would be the 3rd option. This is true because the exterior angle theorem is Proposition 1.16 in Euclid's Elements, which states that the measure of the exterior angle of a triangle is greater than either of the measures of the remote interior angles.

Answer 2

Triangle Exterior Angle Theorem is equal to the sum of the two opposite interior angles. Angle 1 = 60 + 63 = 123 degrees