Answer:
(1) The angles are 81⁰, 76⁰, 23⁰ and y = 157⁰
(2) The angles are E = 122⁰, P = 40⁰, and Q = 18⁰
Step-by-step explanation:
(1)
Considering the first diagram;
(4x + 29) + (5x + 11) + (2x - 3) = 180 (sum of angles in a triangle)
collect like terms together;
(4x + 5x + 2x) + ( 29 + 11 - 3) = 180
11x + 37 = 180
11x = 180 - 37
11x = 143
x = 143 / 11
x = 13
The angles of this triangle are calculated as follows;
4x + 29 = (4 x 13) + 29 = 81⁰
5x + 11 = (5 x 13) + 11 = 76⁰
2x - 3 = ( 2 x 13) - 3 = 23⁰
y⁰ + (2x - 3) = 180 (sum of angles on a straight line)
y⁰ + 23⁰ = 180
y⁰ = 180 - 23
y = 157⁰
(2)
Considering the second triangle;
(15m + 17) + (7m - 9) + (4m - 10) = 180 (sum of angles in a triangle)
(15m + 7m + 4m) + (17 - 9 - 10) = 180
26m - 2 = 180
26m = 180 + 2
26m = 182
m = 182 / 26
m = 7
The angles of this second triangle are calculated as follows;
E: 15m + 17 = (15 x 7) + 17 = 122⁰
P: 7m - 9 = (7 x 7) - 9 = 40⁰
Q: 4m - 10 = ( 4 x 7) - 10 = 18⁰
