Question

Find x and y in the given figures ​

Answer 1

Answer:

i)x= 45°

ii)x= 60°

iii)x= 80.4

iv)x= 30°

Step-by-step explanation:

i) In ∆ AOC, angle O is 90° and AO= OC so angle A = angle C (as angles opposite to equal sides are equal)

By angle Sum Property,

90°+ A + C= 180°

90° + A+ A= 180°

2A= 180° - 90°

A= 90°/2= 45°

x= 45°

ii) Angle subtended by an arc at centre subtends half the angle at other arc.

Angle AOB= 2 angle ACB

40°= 2 angle ACB

angle ACB= 20°

By angle sum Property, in ∆ BDC,

100° + 20° + x= 180°

x= 60°

iii)Angle subtended by an arc at centre subtends half the angle at other arc.

So angle ADB= reflex angle AOB

Angle ADB= 360°- angle AOB

3x-70= 360-2x- 28

3x+2x= 332+70

5x= 402

x= 402/5= 80.4

iv) Angle ACB = 90° ( Angle in semi circle)

As opposite angles of cyclic quadrilateral are supplementary so angle ABC is 60°.

In ∆ ABC, by angle sum Property

90° + 60° + x = 180°

x= 180° - 150°

x= 30°

v)As opposite angles of cyclic quadrilateral are supplementary.

Angle B+ angle D = 180°

3y-5-7x+5 = 180°

3y-7x = 180° ---------1

Angle A+ angle C = 180°

4y+20-4x = 180° ---------2

As RHS of equation 1 and 2 are equal so,

3y-7x = 4y+20-4x

3y-4y= 7x-4x +20

-y= 3x+ 20

y = -3x- 20

Now putting value of y in equation 1

3(-3x- 20)-7x = 180°

-9x -60 - 7x= 180°

-16x = 240°

x= 240°/-16

Hope it helps ☺