Answer:
Measure of angle A = 120°
Measure of angle B = 98°
Measure of angle C = 104°
Measure of angle D = 140°
Step-by-step explanation:
Since the two straight lines are parallel
, then A + 12X =180° (alternate angles)
, then A = 180° - 12X
Since the two straight lines are parallel
, then measure angle A = measure angle (25X-5)°
(opposite angles)
, then 180° - 12X = 25X - 5° (solve it like a normal equation)
, then 180° + 5° = 25X + 12X
, then 185° = 37X
, then X = 185° ÷ 37
= 5
, then measure of angle A = 180° - ( 12 x 5 )
= 180° - 60°
, then measure angle A = 120°
Since the two straight lines are parallel
, then measure angle B = measure angle 14X (corresponding angles)
, then 15X - 7 = 14X
, then 15X - 14X = 7
, then X = 7
Since X =7
, then measure angle B = (15 x 7) - 7
= 105° - 7
, then measure angle B = 98°
Since the two straight lines are parallel
, then measure angle C = 8X
(opposite angles)
, then 5X + 39 = 8X
, 39 = 8X - 5X
, 39 = 3X
, then X = 39 ÷ 3
, X = 13
Since X = 13
, then measure angle C = (5 x 13) +39
= 65 + 39
, then measure angle C = 104°
Since straight that angle D lies on = 180°
, then sum of measure of and D and 4X =
180°
, then (12X + 20) + 4X = 180°
, then 16X + 20 = 180°
, then 16X = 160° (resulting from 180° - 20°)
, then X = 10
Since X = 10
, then 12 x 10 + 20 = 120 + 20
,the measure angle D = 140°
