Answer:
21. x = 11, y = 12
22. x = 22, y = 17
Explanation:
21. See the diagram given with the question.
So, (11x + 5) + (6x - y) = 180 {Those angles are supplementary}
⇒ 17x - y = 175 .......... (1)
⇒ 170x - 10y = 1750 ....... (2)
Again, 11x + 5 = 10y + 6 {Opposite angles are equal}
⇒ 11x - 10y = 1 .......(3)
Now, from equations (3) and (2) we get
170x - 11x = 1750 - 1
⇒ 159x = 1749
⇒ x = 11
Now. from equation (1), we get y = 17x -175 = 187 - 175 = 12 (Answer)
22. Here the diagram is of a rectangle.
Then similar to the previous problem,
2x - 5 = 3y - 12 {Opposite angles are equal}
⇒ 2x - 3y = -7 .......(4)
Again, (7y + x) + (3y - 12) = 180 {Those angles are supplementary}
⇒ 10y + x = 192 ......... (5)
⇒ 20y + 2x = 384 ........ (6)
So, from equations (4) and (6) we get
23y = 391, ⇒ y = 17
Now, from equation (5), we get x = 192 - 10y = 22 (Answer)