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=(1)/(2)(w+79^(\circ))`

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

`\begin{gathered} 110^(\circ)=(1)/(2)(w+79^(\circ)) \\ \text{Cross multiply:} \\ \Rightarrow2*110^(\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.