Question

In fig 10.33, find x. further find angle boc, cod,aod

Answer 1

Given that,

$\angle AOD=(x+10)^{\circ}$

$\angle BOC=(x+20)^{\circ}$

$\angle COD=x^{\circ}$

We need to calculate the value of x

According to figure,

$\angle AOD+\angle COD+\angle BOC=180^{\circ}$

Put the value into the formula

$(x+10)+x+(x+20)=180$

$3x+30=180$

$x=\dfrac{180-30}{3}$

$x=50^{\circ}$

The angle COD is 50°.

We need to calculate the angle AOD and BOC

Using given data

For angle AOD,

$\angle AOD=x+10$

Put the value of x

$\angle AOD=50+10$

$\angle AOD=60^{\circ}$

For angle BOC,

$\angle BOC=x+20$

Put the value of x

$\angle BOC=50+20$

$\angle BOC=70^{\circ}$

Hence, The value of x is 50°.

The angle AOD, BOC and COD are 60°, 50° and 70°.