Question

Hello I really really need help with this question please

Answer 1

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=(1)/(2)m\angle AOB \\ m\angle C=(1)/(2)\cdot120\degree=(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)