In the Figure, lines XY and MN intersect at O. If ∠POY = 90° and
a : b = 2 : 3, find a, b, c and ∠YON
Answers
Answer:
30,45,135
Step-by-step explanation:
since <POY = 90°
<POX= 90°
<POX= <POM+<MOX
90= 2x+3x
90= 6x
x= 15
a:2x= 30 °
b: 3x= 45 °
<MOX + <XON =180° .. linear pair
45 + c= 180
c= 135°
Answer:
C =126°
Step-by-step explanation:
Given:
∠POY= 90° and a : b = 2 : 3
To find:
C
Solution:
If two lines intersect with each other, then the vertically opposite angles formed are equal.
Line OP is perpendicular to line XY. Hence ∠POY = ∠POX = 90°
∠POX = ∠POM + ∠MOX
90° = a + b ….(1)
Since a and b are in the ratio 2 : 3 that is,
a = 2x and b = 3x ….(2)
Substituting (2) in (1),
a + b = 90°
2x + 3x = 90°
5x = 90°
x = 90°/5 = 18°
a = 2x = 2 × 18°
a = 36°
b = 3x = 3 × 18°
b = 54°
Also , ∠MOY= ∠MOP + ∠POY
= a + 90°
= 36° + 90° = 126°
Lines MN and XY intersect at point O and the vertically opposite angles formed are equal.
∠XON = ∠MOY
c = 126°