Question

in this figure XY and MN intersect at O.If angle POY=90° and a:b=2:3 find the value of c
​

Answer 1

Step-by-step explanation:

Let the common ratio between a and b be x. ∴ a = 2x, and b = 3x XY is a straight line, rays OM and OP stand on it. ∴ ∠XOM + ∠MOP + ∠POY = 180º b + a + ∠POY = 180º 3x + 2x + 90º = 180º 5x = 90º x = 18º a = 2x = 2 × 18 = 36º b = 3x= 3 ×18 = 54º ∴ b + c = 180º (Linear Pair) 54º + c = 180º c = 180º − 54º = 126º ∴ c = 126ºRead more on Sarthaks.com - https://www.sarthaks.com/113359/in-the-given-figure-lines-xy-and-mn-intersect-at-o-if-poy-90-and-a-b-2-3-find-c

Answer 2

$\huge{\underline{\underline{\bold{\mathtt{\purple{✍A{\pink{N{\green{S{\blue{W{\red{E{\orange{R✍}}}}}}}}}}}}}}}}$$\huge{\rightarrow}$

• Rᴀᴛɪᴏ = 2:3

Lᴇᴛ ᴀ = 2x

So, ʙ = 3x

A + B + 90° = 180°

• Sᴜᴍ ᴏғ ᴀɴɢʟᴇs ᴏɴ ᴀ sᴛʀᴀɪɢʜᴛ ʟɪɴᴇ = 180°

2x + 3x = 180°

5x = 180°

x = 180/5

x = 36° .

• ᴀ = 2 × 36° = 72°

• ʙ = 3 × 36° = 108°

ʙ + ᴄ = 180°

• sᴜᴍ ᴏғ ᴀɴɢʟᴇs ᴏɴ ᴀ sᴛʀᴀɪɢʜᴛ ʟɪɴᴇ = 180°

108° + ᴄ = 180°

ᴄ = 180° - 108°

ᴄ = 72°