Question

In the diagram, line p is parallel to side BC.

Triangle A B C. Angle A is 2, angle B is 57 degrees, and angle C is 49 degrees. A line p is parallel to side B C at point A to form 3 angles. Angle 2 is angle A, and angle 1 is the exterior angle.

What is the sum of the measures of ∠1 and ∠2?

What is the sum of the measures of Angle1 and Angle2?


mAngle1 + mAngle2 =
°

Answer 1

Given that triangle ABC has angles \( \angle A = 2^\circ \), \( \angle B = 57^\circ \), and \( \angle C = 49^\circ \), we can find the exterior angle at point A created by line \( p \) being parallel to side BC.

In this scenario, \( \angle 1 \) (the exterior angle) is equal to the sum of the two remote interior angles, which are \( \angle B \) and \( \angle C \). Therefore, we calculate:

\[
m\angle 1 = m\angle B + m\angle C = 57^\circ + 49^\circ = 106^\circ
\]

Now, you want to find the sum of \( m\angle 1 \) and \( m\angle 2 \):

\[
m\angle 2 = m\angle A = 2^\circ
\]

Thus, we calculate the sum:

\[
m\angle 1 + m\angle 2 = 106^\circ + 2^\circ = 108^\circ
\]

Therefore, the sum of the measures of \( \angle 1 \) and \( \angle 2 \) is:

\[
m\angle 1 + m\angle 2 = 108^\circ
\]