Question

Geometry question, Lines j and k are parallel. m< 2=(4x-1) and m<6=(y-31) and m<8=105 What is the value of x + y ? And the correct equation for it?

Answer 1

In a set of parallel lines, angle 2 is equal to angle 8 because they are corresponding angles. Angle 6 is equal to angle 8 because they are alternate interior angles. By solving m2 and m6 with the information given, x is found to be 26, y is found to be 136, and their sum x+y is 162.

Step-by-step explanation:

To solve the geometry question involving parallel lines and angles, we need to understand a few concepts of geometry such as alternate interior angles, corresponding angles, and the properties of parallel lines cut by a transversal. The student provided the measures of angles related to these lines: m2 = (4x-1), m6 = (y-31), and m8 = 105. Since lines j and k are parallel, certain angle pairs are congruent. Angle 8 and angle 6 are alternate interior angles, which means that they are equal when the lines are parallel. And angle 2 would be congruent to angle 8 as well since they would be corresponding angles.

Firstly, since m8=105, we can set it equal to m6:

105 = y - 31

Adding 31 to both sides, we get:

y = 136

Similarly, we can set m2 equal to m8 because they are corresponding angles:

(4x-1) = 105

Adding 1 to both sides and then dividing by 4:

x = 26

In conclusion, to find the value of x+y, we add the x value of 26 to the y value of 136:

x+y = 26+136

x+y = 162

The correct equation to find the sum of x and y is:

x+y = (4x-1) + (y-31) when m2 = m8 = 105

Answer 2

The value of x + y is 162.5.

Identify Corresponding Angles: Since lines j and k are parallel, we know that the corresponding angles are congruent. That means:

Angle 2 and Angle 6 are corresponding angles.

Angle 8 and Angle 6 are also corresponding angles.

Set Up Equations: Based on the given information, we can set up two equations:

Equation 1: m∠2 = (4x - 1)°

Equation 2: m∠6 = (y - 31)°

Use the Congruency of Corresponding Angles:

From Equation 1 and Equation 2, we know that m∠2 = m∠6.

Therefore, (4x - 1)° = (y - 31)°.

Use the Given Measure of Angle 8:

We are given that m∠8 = 105°.

Since Angle 8 and Angle 6 are corresponding angles, m∠6 = 105°.

Solve for x and y:

Substitute 105° for m∠6 in the equation (4x - 1)° = (y - 31)°:

4x - 1 = 105

4x = 106

x = 26.5

Substitute 105° for m∠6 in the equation m∠6 = (y - 31)°:

105 = y - 31

y = 136

Find x + y:

x + y = 26.5 + 136 = 162.5