Question

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

Explanation:

Step1: Recall angle - at - the - intersection - of - chords formula

The measure of an 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 arc $AB = 120^{\circ}$ and the arc $CD=z$. The angle $\angle AEB = 112^{\circ}$. According to the formula $\angle AEB=\frac{1}{2}(m\overset{\frown}{AB}+m\overset{\frown}{CD})$.

Step2: Substitute the known values into the formula

We know that $112^{\circ}=\frac{1}{2}(120^{\circ}+z)$. First, multiply both sides of the equation by 2 to get rid of the fraction: $2\times112^{\circ}=120^{\circ}+z$.

Step3: Solve for $z$

$224^{\circ}=120^{\circ}+z$. Then subtract $120^{\circ}$ from both sides: $z = 224^{\circ}-120^{\circ}=104^{\circ}$.

Answer:

$104^{\circ}$