Question

Hello I really really need help with this question please

Answer 1

Solution:

Given a circle with the measures of angle given below

$\begin{gathered} m\angle A=42\degree \\ arc\text{ AB}=120\degree \end{gathered}$

The redrawn figure is shown below

$arc\text{ AB}=m\angle AOB=120\degree$

Applying the circle theorem,

The angle at the center is twice the angle at the circumference, i.e

$\begin{gathered} m\angle C=\frac{1}{2}m\angle AOB \\ m\angle C=\frac{1}{2}\cdot120\degree=\frac{120}{2}=60\degree \\ m\angle C=60\degree \end{gathered}$

To find m∠B, we will apply the sum of angles in a triangle, i.e.

$\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ 42\degree+m\angle B+60\degree=180\degree \\ m\angle B+102\degree=180\degree \\ Collect\text{ like terms} \\ m\angle B=180\degree-102\degree \\ m\angle B=78\degree \end{gathered}$

Hence, m∠B = 78° (option C)