Question

In figure, lines XY and MN intersect at O. If Poy =90 and a:b= 2:3,find c.

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Answer 1

Answer:

poy=90

so, pox=90 (linear pair)

pox= a+b

= 2x+3x

>5x=90

> x= 90/5

x= 18

hence, a= 2*18

= 36

b= 3*18

= 54

Now,

b+c= 180 (linear pair)

c= 180-54

= 126

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Answer 2

Question ::-

In figure, lines XY and MN intersect at 0. If ∠POY = 90° , and a : b = 2 : 3. find c?

Given ::-

• lines XY and MN intersect at 0

• ∠POY = 90°

• a : b = 2 : 3

To find ::-

• a : b = 2 : 3. find 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°

__________

$From \: (ii), \: we \: get$

$b = 32 \times 36° = 54°$

$Since \: XY \: and \: MN \: interstect \: at \: O,$

$∴ c = \: (a +∠POY)[Vertically \: opposite \: angles]$

$or \: \: c = 36° + 90° = 126°$

Thus, the required measure of c = 126°.