Question

70 POINTS PLEASE HELP
1. Use complete sentences to explain how the special angles created by the intersection of and by can be used to solve for x .
2. Solve for x, showing all of your work.
Find the measure of angle 6

Answer 1

The value of x = 24, and the measure of angle 6 is 79°.

Given:

Two parallel lines A and B and a transversal D

To Find:

The value of x =?

The measure of angle 6 is?

Solution:

(1) If two lines are parallel, then the sum of their co-interior or co-exterior angles 180°.

As we can see from the figure given in the question, line A is parallel to line B and line D is transversal.

The sum of the angles of 3x + 4\7 and 4x + 5 will be 180° as these angles are co-exterior angles.

Using this property, we can solve for x.

(2) 3x + 7 + 4x + 5 = 180° (the angles are co-exterior angles)

⇒ 7x + 12 = 180

⇒ 7x = 180 - 12

⇒ 7x = 168

∴ x = 24

(3) 4x + 5 = 4 × 24 + 5 = 96 + 5 = 101°

101° and angle 6 are supplementary angles. It means the sum of these angles is 180°.

So, 101° + ∠6 = 180°

⇒ ∠6  = 180° - 101°

∴ ∠6 = 79°

Hence, the value of x = 24, and the measure of angle 6 is 79°.

#SPJ1

Answer 2

Answer:

$\boxed{\begin{aligned}& \qquad \:\sf \:x = 24 \qquad \: \\ \\& \qquad \:\sf \: \angle \: 6 = 79^{ \circ}\end{aligned}} \qquad$

Step-by-step explanation:

Given that line A is parallel to line B.

Now, line A is parallel to line B and line C acts as transversal.

We know, pair of corresponding angles are equal.

$\implies\sf \: \angle \:6 = (3x + 7)^{ \circ} - - - (1)$

Now, D is a line.

So,

$\implies\sf \: \angle \: 6 + 4x + 5 = 180$

$\sf \:3x + 7 + 4x + 5 = 180$

$\sf \:7x + 12 = 180$

$\sf \:7x = 180 - 12$

$\sf \:7x = 168$

$\sf \: x = \dfrac{168}{7}$

$\implies\sf \: \boxed{\bf \: x = 24 \: }$

On substituting the value of x in equation (1), we get

$\sf \: \angle \:6 = 3 \times 24 + 7$

$\sf \: \angle \:6 = 72 + 7$

$\implies\bf \: \angle \: 6 = {79}^{ \circ}$

Hence,

$\implies\sf \: \boxed{\begin{aligned}& \qquad \:\sf \:x = 24 \qquad \: \\ \\& \qquad \:\sf \: \angle \: 6 = 79^{ \circ}\end{aligned}} \qquad$