Answer:
[tex](a)[/tex]
[tex]x = 18.5[/tex]
[tex]y = 22.5[/tex]
[tex](b)[/tex]
[tex]x = 10[/tex]
Step-by-step explanation:
Solving (a):
7x - 19 and 3x + 14 are interior angles.
So:
[tex]7x - 19 + 3x +14 = 180[/tex]
Collect like terms
[tex]7x + 3x = 180 - 14 + 19[/tex]
[tex]10x = 185[/tex]
[tex]x = 18.5[/tex]
7x - 19 and 5y - 2 are equal angles --- corresponding angles
So:
[tex]5y - 2 = 7x - 19[/tex]
Make 5y the subject
[tex]5y = 7x - 19+2[/tex]
5y = 7x -17
Make y the subject
[tex]y = \frac{1}{5} (7x - 17)[/tex]
Substitute [tex]x = 18.5[/tex]
[tex]y = \frac{1}{5} (7*18.5 - 17)[/tex]
[tex]y = \frac{1}{5} (112.5)[/tex]
[tex]y = 22.5[/tex]
Solving (b):
The triangle is right-angled.
So:
[tex]5x + 3 + 2x + 17 + 90 = 180[/tex]
Collect Like Terms
[tex]5x + 2x = 180 - 90 - 17-3[/tex]
[tex]7x = 70[/tex]
[tex]x = 10[/tex]
