Question

Lines b and c are parallel. Horizontal and parallel lines b and c are cut by transversal a. Where line b intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, (18 x + 4) degrees, (7 x + 1) degrees. Where line c intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. What is the measure of Angle2? mAngle2 = 31° mAngle2 = 50° mAngle2 = 120° mAngle2 = 130°

Answer 1

Answer:

mAngle2 = 50°

Step-by-step explanation:

A relative schematic has been attached bellow describing the problem.

In this case, we will be working with Supplementary angles. The latter denote angles which when summed together equal to 180°.

From the schematic we can identify the following Supplementary pairs as:

∠1 and ∠2

∠2 and ∠(18x+4)

∠(18x+4) and ∠(7x+1)

∠(7x+1) and ∠1

So lets start by finding the value of $x$ as follow. Since we know the supplementary pairs we have that

$(18x+4)+(7x+1)=180\\18x+7x+4+1=180\\25x+5=180\\25x=180-5\\25x=175\\x=\frac{175}{25} \\x=7$

Now we similarly know that ∠2 and ∠(18x+4) are supplementary. So lets replace the value of $x$ in ∠$18x+4$, we have

$18(x=7)+4=126+4=130$

So finally we have

Thus we can say that ∠2 = 50° (which matches the second options from the available ones).

Answer 2

Answer:

50

Step-by-step explanation: