Question

I really need some math help. How do I do this?

Answer 1

First, find the value of x. Then, use the measures of the arcs to find the value of w.

When two chords intersect, the measure of the internal angle is equal to the average of the arcs that it encloses:

$c=\frac{1}{2}(a+b)$

Since the angle of 70° encloses arcs of 60° and x°, then:

$70=\frac{1}{2}(60+x)$

Solve for x:

$\begin{gathered} x=2\times70-60 \\ =140-60 \\ =80 \end{gathered}$

The sum of the measures of the arcs of a circle must be equal to 360°. Then:

$w+x+79+60=360$

Substitute x=80 and solve for w:

$\begin{gathered} \Rightarrow w+80+79+60=360 \\ \Rightarrow w+219=360 \\ \Rightarrow w=360-219 \\ \Rightarrow w=141 \end{gathered}$

Therefore, the value of w is:

$141^{\circ}$