Question

Please help me find the value of x in this picture

Answer 1

Given:

m∠D = 5x - 10

m(ar EC) = 60°

m(ar RB) = 13x + 7

To find:

The value of x.

Solution:

If two secants intersect outside a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

`$\Rightarrow \angle D = (1)/(2) (m \ ar(RB) - m \ ar(EC) )`

`$\Rightarrow 5x-10 = (1)/(2) (13x+7 - 60 )`

`$\Rightarrow 5x-10 = (1)/(2) (13x-53 )`

Multiply by 2 on both sides.

`$\Rightarrow 2* ( 5x-10) = 2 * (1)/(2) (13x-53 )`

`$\Rightarrow 10x-20 =13x-53`

Add 53 on both sides, we get

`$\Rightarrow 10x+33 =13x`

Subtract 10x on both sides, we get

`$\Rightarrow 33 =3x`

Divide by 3 on both sides, we get

`$\Rightarrow 11=x`

The value of x is 11.