Question

properties of parallel lin
guided practice
find the measure of \\( \angle 2 \\) in the figure.
\\( 110 ^ { 0 } \\)
\\( 10 ^ { \circ } \\)
\\( 80 ^ { \circ } \\)
\\( 70 ^ { \circ } \\)

Explanation:

Step1: Calculate the sum of interior angles of quadrilateral

The sum of interior angles of a quadrilateral is \((4 - 2)\times180^{\circ}=360^{\circ}\).

Step2: Find the adjacent angle of \(70^{\circ}\)

The adjacent angle of \(70^{\circ}\) is \(180^{\circ}- 70^{\circ}=110^{\circ}\).

Step3: Calculate \(\angle2\)

Let \(\angle2=x\). We know \(\angle A = 80^{\circ}\), \(\angle1\) and \(\angle A\) are supplementary (because \(AB\parallel DC\)), so \(\angle1=180^{\circ}-80^{\circ} = 100^{\circ}\).
Using the sum of interior angles of quadrilateral \(ABCD\): \(80^{\circ}+100^{\circ}+110^{\circ}+x=360^{\circ}\).
Simplify the left - hand side: \(290^{\circ}+x=360^{\circ}\).
Solve for \(x\): \(x = 360^{\circ}-290^{\circ}=70^{\circ}\).

Answer:

\(70^{\circ}\)