Question

friday 8.g.5
1.)
lines ( l _ { 1 } ) and ( l _ { 2 } ) are parallel and ( l _ { 3 } ) is a transversal.
if ( m angle 1 ) is ( 110 ^ { circ } ), what is ( m angle 2 ) ?
a ( 50 ^ { circ } )
b ( 90 ^ { circ } )
c ( 110 ^ { circ } )
d ( 170 ^ { circ } )
2.)
triangle ( a b c ) is shown. the measure of the interior angle at po
exterior angle at point ( c ) is ( 102 ^ { circ } ).
what is the measure of angle ( x ) ?
a ( 62 ^ { circ } )
b ( 78 ^ { circ } )
c ( 102 ^ { circ } )
d ( 118 ^ { circ } )

Explanation:

Step1: Find the measure of ∠3

Since ∠1 and ∠3 are supplementary (they form a linear pair), we know that \(m\angle1 + m\angle3=180^{\circ}\). Given \(m\angle1 = 110^{\circ}\), then \(m\angle3=180^{\circ}- 110^{\circ}=70^{\circ}\).

Step2: Use the property of parallel lines

Because \(l_1\parallel l_2\) and \(l_3\) is a transversal, ∠3 and ∠4 are alternate - interior angles. So \(m\angle4 = m\angle3 = 70^{\circ}\).

Step3: Find the measure of ∠2

Since ∠4 and ∠2 are supplementary (they form a linear pair), \(m\angle2=180^{\circ}-m\angle4\). Substituting \(m\angle4 = 70^{\circ}\), we get \(m\angle2 = 110^{\circ}\).

For problem 2:

Step1: Find the interior angle at \(C\)

The interior angle at \(C\) and the exterior angle at \(C\) are supplementary. Let the interior angle at \(C\) be \(y\), then \(y + 102^{\circ}=180^{\circ}\), so \(y = 78^{\circ}\).

Step2: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. In \(\triangle ABC\), \(x=40^{\circ}+78^{\circ}\).

Answer:

1. \(C\)
2. \(D\)