in fig lines XY and MN intersect each other at point O. If angle POY= 90° and a:b = 2:3 then the value of angle C is
Answers
Answer:
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°
Answer:
Step-by-step explanation:
Linear pair of angles:
If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.
Axiom- 1
If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.
Axiom-2
If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.
The two axioms given above together are called the linear pair axioms.
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Solution:
Given,
∠POY = 90° &
a : b = 2 : 3
A.T.Q
∠POY+∠POX =180°
[By linear pair axiom]
∠POY + a + b = 180°
⇒ 90° + a + b = 180°
⇒ a + b = 90°
Let a = 2x & b= 3x
2x + 3x = 90°
⇒ 5x = 90°
⇒ x = 18°
∴ a = 2×18° = 36°
b = 3×18° = 54°
Now, OX is a ray on the line MON.
∠XOM + ∠XON=180°
b + c = 180° (by Linear Pair axiom)
⇒ 54° + c = 180°
⇒ c = 126°
The value of c =126°
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Hope this will help you...