Question

Two alternate exterior angles are formed by a transversal through two parallel lines. If one of these alternate exterior angles has an angle measure of , and the other angle has a measure of , then what is the sum of their angle measures

Answers

  1. The sum of the angle measures of the exterior angles is 180.

    What is an exterior angle?

    The exterior angle refers to the angle between a side of a polygon and an extended adjacent side.
    Now, given that 5x-21 and 2x+12 are two alternate exterior angles. We know that the sum of the two exterior angles is 180° because the two exterior angles are lying on a straight line and straight line is 180°.
    Thus, (5x-21)+(2x+12) = 180°
    => 5x-21+2x+12 = 180
    => 5x+ 2x -21 +12 = 180
    => 7x – 9 = 180
    =>7x = 189
    => x = 189/7 = 27
    Hence the angles are:
    1. 5x-21 = (5*27) – 21 = 135 – 21 = 114
    1. 2x+12 = 2 * 27 + 12 = 54+12 = 66
    And sum = 114+66= 180  
    To learn more about exterior angles from the given link:
    #SPJ4

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