Question

In Fig. 6.14, lines XY and MN intersect at 0. If
POY = 90° and a : b= 2:3, find c. ​

Answer 1

Answer:

a=2

b=3

poy=90

let us assume,

a=2x

b=3x

straight angle cintains 180

2x+3x+90=180

5x+90=180

5x=180-90

5x=90

x=90/5

x=18

then,

a=2x=2×18=36

b=3x=3×18=54

let us assume that the angle beaide angle"c" is angle d

ANGLE B=ANGLE D(opposite angles)

so,angle b is 54 then angle d is also 54 degrees

so angle c is what?

its very simple, we got the angleD

XY is a linear angle=180

c+d=180

c+54=180

c=180-54

c=126 degrees

Answer 2

Answer:

• c = 126 °

Step-by-step explanation:

Given :-

• ∠POY= 90° and a : b = 2 : 3

To Find :-

find the c ?

• We know that, If two lines intersect with each other, then the vertically opposite angles formed are equal.

Solution :-

Given, ∠ POY = 90 °

: $\implies$ a : b = 2 : 3

: $\implies$ c = ?

Let the ratio be x a = 2 x , 2 x + 3 x = 90° ( ∠ POX = 90°)

: $\implies$ 5 x = 90

: $\implies$ x = 90 / 5

: $\implies$ = 18

: $\implies$ x = 18

: $\implies$ a = 2 x = 2 × 18 = 36

: $\implies$ b = 3 x = 3 × 18 = 54

: $\implies$ b = 3 x

: $\implies$ In MON

: $\implies$ ∠ XOM + ∠ XON = 180 °

: $\implies$ 54 ° + ∠ XON = 180 °

: $\implies$ ∠ XON = 180 - 54

: $\implies$ = 126°

Know more :

Acute Angle: An Acute Angle is an angle whose angle measures less than 90 degrees. Such angles as 60 degrees, 50 degrees, etc. are acute angles.

Right Angle: A Right Angle is an angle that measures exactly 90 degrees. The angle at 90 degrees is always a right angle.

Obtuse Angle: Obtuse Angle is an angle whose angle measures between 90 degrees to 180 degrees. Angles at 120 degrees, 150 degrees, etc. are Obtuse Angles.

Straight Angle: A Straight Angle is an angle whose angle measures exactly 180 degrees. This is called a straight angle.

Reflex Angle: A Reflex Angle is an angle whose angle measures between 180 degrees to 360 degrees. Angles at 200 degrees, 260 degrees, etc. are Reflex Angles.

Complete Angle: A Complete Angle is an angle whose angle measures exactly 360 degrees. This is called a complete angle.