96.9k views
1 vote
Hello I really really need help with this question please

Hello I really really need help with this question please-example-1
User Neuro
by
7.7k points

1 Answer

2 votes

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=(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)

Hello I really really need help with this question please-example-1
User Wouter Verlaek
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories