PLEASE HELP I HAVE A TIMER
In the diagram, the measure of angle 1 is (3x)°, and the measure of angle 2 is (12x)°

A transversal intersects 2 lines to form 8 angles. Clockwise from the top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8.

What is the measure of angle 4?
36°
45°
135°
144°

Answer:

144 degrees.

Step-by-step explanation:

Draw yourself a diagram with 2 horizontal lines and a transversal cutting across it.

After labeling, you will see that angle 4 is the same as angle 1. You can also see that angle 1 and 2 add up to 180, as they are sitting on a straight line.

First, before we get to the angle of 4, we have to find the value of x:

1) angle 1 + angle 2 = 180

3x + 12x = 180

2) solve the above equation for x

15x = 180

3) divide both sides by 15 for x

x= 12 degrees

We know that angle 4 is the same as angle 2, which is 12x degrees.

So, now that we know what x is, 12 x 12 degrees =  144 degrees.

Hope this helped : )

The measure of angle ∠4 is 144°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

The measure of angle 1 = ( 3x )°

The measure of angle 2 = ( 12x )°

Angle 1 and Angle 2 are on the straight lines

So , the sum of the measures of angles = 180°

On simplifying the equation , we get

3x + 12x = 180

15x = 180

Divide by 15 on both sides of the equation , we get

x = 12

Substituting the value of x in the equation , we get

The measure of angle 2 = measure of angle 4 ( corresponding angles )

So , the measure of angle 4 = ( 12x )°

And , the measure of angle ∠4 = 144°

Hence , the angle ∠4 = 144°

To learn more about parallel lines cut by transversal click :

https://brainly.com/question/28182928

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