Question

In the diagram, the measure of angle 2 is 126°, the measure of angle 4 is (7x)°, and the measure of angle 5 is (4x + 4)°.

Answer 1

7x=126
x=18
angle 5= 4(18) +4 = 76
angle 7 = 76

Answer 2

Answer:

The measure of angle 7 is 76°.

Step-by-step explanation:

If two lines intersect each other, then the alternative angles are known as vertically opposite angles.

The vertically opposite angles are always congruent.

From the given figure it is noticed that the angle 2 and 4 are vertically opposite angles.

$\angle 2=\angle 4$

$126=7x$

Divide both sides by 7.

$x=18$

The value of x is 18.

From the given figure it is noticed that the angle 5 and 7 are vertically opposite angles.

$\angle 5=\angle 7$

$\angle 7=4x+4$

Substitute x=18.

$\angle 7=4(18)+4$

$\angle 7=72+4$

$\angle 7=76^{\circ}$

Therefore the measure of angle 7 is 76°.