Question

guys please solve 17 ; 18;19

Answer 1

Q17.   Since AB//CD,angle BAO=x....interior opp. Angle ,so in triangleBOA y+x=z.....by exterior angle property

Answer 2

A.17

Given:AB ll CD,

To Prove :z=x+y

Proof: In the given figure, AB llCD

So, y=<OCD

In Triangle OCD

<x+<y+<COD=180                 [Angle Sum Property]

=> <COD=180-(x+y)                   .....................Eq.(1)

=> <COD+z=180                   [Linear Pair]

From Eq.(1)

=>180-(x+y)+z=180

=> -(x+y)+z=180

So, x+y=z.

A.18

Let there be a isosceles triangle ABC, such that AB=AC.

So,<ABC=<ACB

It is given that the base angle is 15° more than the vertical angle,

So if we assume that <BAC=x

=> <ABC=<ACB=x+15

<ABC+<ACB+<BAC=180          [Angle sum Property]

Substituiting their values we get

=>x+x+15+x+15=180

=>3x+30=180

=>3x=150

So,x=50°=<BAC

=>x+15=65°=<ABC=<ACB.

A.19

Let there be a isosceles triangle ABC, such that AB=AC.

So,<ABC=<ACB

Let the base angle be x, => <ABC=<ACB=x

It is given that the vertical angle is twice the sum of its base angles,

So, <BAC=2(x+x)=4x

Now,<BAC+<ABC+<ACB=180       [Angle sum Property]

On substituiting their values we get,

=>x+x+4x=180

=>6x=180

=>x=30°

=> <ABC=<ACB=x=30°

<BAC=4*x=4*30=120°.

Thanks!!!