Question

what is the value of z? 52° 104° 116° 208° 120° 112°

Explanation:

Step1: Recall angle - of - intersecting - chords formula

The measure of the angle formed by two intersecting chords in a circle is given by $\frac{1}{2}$ the sum of the measures of the intercepted arcs. Let the arcs be $x$ and $y$. If the angle formed by the chords is $\theta$, then $\theta=\frac{1}{2}(x + y)$. Here, the angle $\angle AEB=112^{\circ}$, and the intercepted arcs are $120^{\circ}$ and $z$.

Step2: Apply the formula

We know that $\angle AEB=\frac{1}{2}(120 + z)$. Since $\angle AEB = 112^{\circ}$, we can set up the equation $112=\frac{1}{2}(120 + z)$.

Step3: Solve the equation

Multiply both sides of the equation by 2: $112\times2=120 + z$. So, $224=120 + z$. Then subtract 120 from both sides: $z=224 - 120$.

Answer:

$z = 104^{\circ}$