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Answer:

10)
\sf x = -8

11)
\sf x = 4

Explanation:

10)

Co-interior angles are angles that are located on the same side of a transversal and between two parallel lines. Co-interior angles are supplementary, which means that they add up to 180 degrees.

In the given case,
\sf x + 78 and
\sf x + 118 are co-interior angles. This means that their measures add up to 180 degrees.

Therefore, we can write the equation:


\sf x + 78 + x + 118 = 180^\circ

Combining like terms, we get:


\sf 2x + 196 = 180^\circ

Subtracting 196 from both sides of the equation, we get:


\sf 2x + 196-196 =( 180-196)^\circ


\sf 2x = -16

Dividing both sides of the equation by 2, we get:


\sf (2x )/(2)=( -16)/(2)


\sf x = -8

Therefore, the measures of x is -8.

11)

Alternate angles are angles that are located on the opposite sides of a transversal and between two parallel lines. Alternate angles are congruent, which means that they have the same measure.

In the given case,
\sf 12x + 2 and
\sf 50^\circ are alternate angles.

This means that their measures are equal.

Therefore, we can write the equation:


\sf 12x + 2 = 50^\circ

Subtracting 2 from both sides of the equation, we get:


\sf 12x + 2-2 =( 50-2)^\circ


\sf 12x = 48

Dividing both sides of the equation by 12, we get:


\sf ( 12x )/(12)= (48)/(12)


\sf x = 4

Therefore, the measure of x is 4.

User Jasmen
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