Given:
The figure of a circle.
Measure of arc = 176°
Measure of angle = (27x+7)°
To find:
The value of x.
Solution:
We know that the measure of central angle is equal to measure corresponding intercepted arc and the measure of central angle is twice of the measure of subtended angle on that arc.
So, the measure of arc is twice of measure of subtended angle on that arc.
[tex]m(arc FH)=2\times m\angle FGH[/tex]
[tex]176^\circ=2\times (27x+7)^\circ[/tex]
[tex]\dfrac{176^\circ}{2}=(27x+7)^\circ[/tex]
[tex]88^\circ=(27x+7)^\circ[/tex]
Now,
[tex]88=27x+7[/tex]
[tex]88-7=27x[/tex]
[tex]\dfrac{81}{27}=x[/tex]
[tex]3=x[/tex]
Therefore, the value of x is 3.