Question

In the following diagram, A | B. A 3x+7 22 23 B 24 26 25 4x+5 C 5y-2927 28 3y+19 D 1. Use complete sentences to explain how the special angles created by the intersection of A and B by D can be used to solve for c. 2. Solve for 2, showing all of your work. 3. Find the measure of 26.

Answer 1

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Since lines A and B are parallel, then the angles <1 and <4 are called corresponding angles, and are equal in measure. Also the same goes for angles <2 and <5 (corresponding angles and therefore equal in measure)

The angles opposed by the vertex (like <2 and angle of measure 3x+7 must be equal. Angles opposed by the vertex <1 and <3 are also equal, as well as angles <5 = <6, and <4 = 4x+5(all of these opposed by the vertex.

We are asked to solve for <2 and angle <6. We now as well that <6 plus 4x+5 must render 180 degrees because they add to give a straight line. And angle 6 must be equal in measure to 3x+7 because they are corresponding angles. Then we have the following equation:

4 x + 5 + 3 x + 7 = 180

and we can solve for "x" in the equation:

7 x + 12 = 180

subtract 12 from both sides:

7 x = 180 - 12

7 x = 168

divide both sides by 7:

x = 168 / 7

x = 24

SInxe x = 24 degrees, then we know the valueof angle <2 which equals 3 x + 7:

<2 = 3 (24) + 7 = 79 degrees

And angle <6 should be equal to angle <2 since they are alternate internal angles between parallel lines. Then <6 = 79 degrees as well.