Question

Lines q and r are parallel. Parallel lines q and r are cut by transversals s and t. The angles formed by the intersection of lines q, s, and t, clockwise from top left, are blank, 53 degrees, blank, 57 degrees, blank, blank; formed by s and r are blank, 5 x degrees, blank, blank. What is the value of x? 14 22 53 70.

Answer 1

Alternate Interior Angles are formed on the interior of the parallel lines, on the opposite sides of the transverse. The value of x is 14.

What are Alternate interior angles?

When two parallel lines are cut by a transverse. the angles formed on the interior of the parallel lines, on the opposite sides of the transverse are known as the Alternate Interior Angle.

As we can see in the centre where the triangle is formed, the measure of the different angles can be written as,

Vertically opposite Angles, $\angle A = 53^o$

Alternate Interior Angles, $\angle C = 57^o$

$\angle B = 5x$

Now, the sum of all the angles of this triangle can be written as,

$\angle A+\angle B+\angle C = 180^o\\\\53^o + 5x + 57^o = 180^o\\\\110^o + 5x = 180^o\\\\5x = 180^o-110^o\\\\5x = 70^o\\\\x = 14$

hence, the value of x is 14.

Learn more about Alternate Interior Angles:

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Answer 2

Answer:

22

Step-by-step explanation: