Question

What is the value of a + b+c? you may assume that the ray is tangent to the circle?a. 86b.150c.133d.47

Answer 1

ANSWER:

c. 133°

STEP-BY-STEP EXPLANATION:

We have that there is a chord that divides the circle in two equal parts because it passes through the middle of the circle. Since it is half of the circle, the arc is 180°, we can see that this arc is the sum of the angles a + b, this angle must measure half of 180°, therefore:

$a\degree+b\degree=\frac{180\degree}{2}=90\degree$

Now the angle c° must measure half of the 86° arc, therefore:

$\begin{gathered} c\degree=\frac{86\degree}{2}=43\degree \\ \end{gathered}$

That means that a° + b° + c° is equal to:

$a°+b°+c°=90+43=133\degree$

Therefore, the correct answer is c. 133°