Question

Find the value of x.
Answer options: 82, 88, 76, 94

Answer 1

Answer:

x = 76°

Step-by-step explanation:

We can solve this by using the angles of intersecting chords theorem. This tells us that when two chords intersect inside a circle, the angle formed is half of the sum of the intercepted arcs of the angle.

This implies that the angle 94° should be half of the sum of Arc measuring x° and the arc measuring 112°. So we can write the equation as:

$94=\frac{1}{2}(x+112)$

We can simplify and solve for x:

$94=\frac{1}{2}(x+112)\\\\94=\frac{1}{2}x+56\\94-56=\frac{1}{2}x\\38=\frac{1}{2}x\\x=38*2=76$

Hence, x = 76°