Question

In the figure, lines XY and MN intersect at O.if POY = 90° and a : b= 2:3. find the value of c.​

Answer 1

Step-by-step explanation:

angle C =126,angle A=36,angle B=54

Answer 2

Question :-

In the figure, lines XY and MN intersect at O.if POY = 90° and a : b= 2:3. find the value of c.

Solution :-

Since XOY is a straight line.

∴ b+a+∠POY= 180°

But ∠POY = 90° [Given]

∴ b + a = 180° – 90° = 90° …(i)

Also a : b = 2 : 3 ⇒ b = $\dfrac{3a}{2}$ …(ii)

Now from (i) and (ii), we get

⇒ $\dfrac{3a}{2}$ + A= 90°

⇒ $\dfrac{5a}{2}$ = 90°

⇒ a = $\dfrac{90°}{5}$ × 2

= 36∘

From (ii), we get

b = $\dfrac{3}{2}$ x 36°

= 54°

Since XY and MN interstect at O,

∴ c = [a + ∠POY]

[Vertically opposite angles]

or c = 36° + 90° = 126°

Thus, the required measure of c

= 126°.