Question

Geometry homework due tonightttt worth 50 points

Answer 1

1. m∠2 = 104°
2. m∠3 = 76°
3. m∠4 = 104°

Explanation:

Concept:

Here, we need to know the idea of supplementary angles and linear pairs.

Supplementary angles are two angles or arcs whose sum is 180 degrees.

A linear pair of angles are formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees.

Linear pair and supplementary angles are conveying the same meaning. However, linear pair is describing the "appearance" of the two angles as they form a line which is 180 degrees. On the other hand, supplementary angles are the properties stating two angles adds up to 180 degrees, but are not required to be together.

If you are still confused, you can refer to the attachment below for a graphical explanation.

Solve:

∠1 and ∠2 are linear pairs and supplementary to each other forming 180°

• m∠2 = 180 - 76 = 104°

∠2 and ∠3 are linear pairs and supplementary to each other forming 180°

• m∠3 = 180 - 104 = 76°

∠3 and ∠4 are linear pairs and supplementary to each other forming 180°

• m∠4 = 180 - 76° = 104°

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

Angle 2 = 180 - 76 = 104 (linear pair)

angle 3 = 76 (vertically opposite angles)

angle 4 = 104(vertically opposite angles)