Question

Use the figure to find the measures of the numbered angles. b a t 999 3 7 $ 75 21= 0°, 22 = 0°, 23= 0°, 24 = 0°, 25 = 1,26 = 26= 0°, 27 = 0°

Answer 1

angle 2 and angle 99 are vertically opposite angles. Vertically opposite angles are equal. This means that

angle 2 = 99 degrees

angle 1 and angle 99 are linear pairs. This means that their sum is 180 degrees. Thus,

angle 1 + 99 = 180

angle 1 = 180 - 99

angle 1 = 81 degrees

angle 3 = angle 1 because they are vertically opposite

angle 3 = 81 degrees

Line a and b are parallel and line t is the transversal. angle 1 and angle 5 are corresponding angles because they have similar position and lie on the same side of the transversal. Corresponding angles are equal. Thus,

angle 5 = angle 1

angle 5 = 81 degrees

angle 2 and angle 6 are corresponding angles

angle 2 = angle 6

angle 6 = 99 degrees

angle 2 and angle 4 are alternate interior angles. they lie on alternate sides of the transversal. alternate angles are equal. Thus,

angle 2 = angle 4

angle 4 = 99 degrees

angle 7 and angle 6 are linear pairs. thus

angle 7 = 180 - angle 6 = 180 - 99

angle 7 = 81 degrees