Question

I just need a brief explanation with the answer.For the second blank the answer choices are-21,3,6,18For the third blank the answer choices are -60,75,45,30

Answer 1

To determine the measure of angles in the triangle below:

Alternate interior angles are congruent, meaning they have equal measure. When we have two parallel lines that are intersected by a transversal, and again my parallel lines are identified by using the same number of arrows, then two special angles are congruent and that is alternate interior angles.

The diagram above is shwoing two parallel lines for an alternate interior angles theorem states that, the alternate interior angles are congruent when the transversal intersects two parallel lines.

Therefore the diagram illustrates Alternate interior angles are congruent

Hence the correct answer is Option B

`\begin{gathered} 4x-12=3x+6 \\ \text{collect like terms} \\ 4x-3x=6+12 \\ x=18 \end{gathered}`

Therefore the value of the x = 18

The measure value of the alternate interior angle = 4x-12

`\begin{gathered} 4x-12 \\ 4(18)-12 \\ 72-12=60 \end{gathered}`

The measure value of the alternate interior angle = 60