Question

in the diagram, what is the measure of angle 1 to the nearest degree? 82° 92° 94° 98°

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So \(7x + 4=88\).
Solve for \(x\):
\(7x=88 - 4\)
\(7x=84\)
\(x = 12\).

Step2: Find the measure of \((7x-2)^{\circ}\)

Substitute \(x = 12\) into \(7x-2\):
\(7\times12-2=84 - 2=82\).

Step3: Use linear - pair property

Since angle \(1\) and \((7x - 2)^{\circ}\) form a linear pair (\(\angle1+(7x - 2)=180\)).
Substitute \(7x - 2 = 82\) into the equation:
\(\angle1+82=180\).
\(\angle1=180 - 82\).

Answer:

\(98^{\circ}\)