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.
[tex]$\Rightarrow \angle D = \frac{1}{2} (m \ ar(RB) - m \ ar(EC) )[/tex]
[tex]$\Rightarrow 5x-10 = \frac{1}{2} (13x+7 - 60 )[/tex]
[tex]$\Rightarrow 5x-10 = \frac{1}{2} (13x-53 )[/tex]
Multiply by 2 on both sides.
[tex]$\Rightarrow 2\times ( 5x-10) = 2 \times \frac{1}{2} (13x-53 )[/tex]
[tex]$\Rightarrow 10x-20 =13x-53[/tex]
Add 53 on both sides, we get
[tex]$\Rightarrow 10x+33 =13x[/tex]
Subtract 10x on both sides, we get
[tex]$\Rightarrow 33 =3x[/tex]
Divide by 3 on both sides, we get
[tex]$\Rightarrow 11=x[/tex]
The value of x is 11.
