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.

$\Rightarrow \angle D = \frac{1}{2} (m \ ar(RB) - m \ ar(EC) )$

$\Rightarrow 5x-10 = \frac{1}{2} (13x+7 - 60 )$

$\Rightarrow 5x-10 = \frac{1}{2} (13x-53 )$

Multiply by 2 on both sides.

$\Rightarrow 2\times ( 5x-10) = 2 \times \frac{1}{2} (13x-53 )$

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

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.