Question

I need help on in the answer to this question

Answer 1

Notice that angle z and the angle with measure 70⁰ is a linear pair. Hence, it follows that they are supplementary (they'll sum up to 180⁰):

$z+70^{\circ}=180^{\circ}$

Solve for z in the equation:

$\begin{gathered} z=180^{\circ}-70^{\circ} \\ \Rightarrow z=110^{\circ} \end{gathered}$

Using the Angles formed by two intersecting chords theorem: If two chords intersect inside a circle, then the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle , it follows that:

$z=\frac{1}{2}(w+79^{\circ})$

Substitute z=110⁰ into the equation and solve for w:

$\begin{gathered} 110^{\circ}=\frac{1}{2}(w+79^{\circ}) \\ \text{Cross multiply:} \\ \Rightarrow2\times110^{\circ}=w+79^{\circ} \\ \Rightarrow220^{\circ}=w+79^{\circ} \\ \Rightarrow w=220^{\circ}-79^{\circ} \\ \Rightarrow w=141^{\circ} \end{gathered}$

The value of w is 141.