f two interior angles on the same side of a transversal intersecting two parallel lines are in ratio 2 :3 then, what is the smaller anlge?

The two interior angles on the same side of a transversal intersecting two parallel lines

add up to 180°
let the angles be 2x and 3x
2x+3x = 180
x = 36

So the angles are .....

Let the angles be 2 x and 3 x

Sum of interior angles on same side of transversal intersecting two parallel lines is 180°

2 x + 3 x = 180°

5 x = 180°

x = 180° / 5 = 36°

The angles are:

2 x = 2 ∙ 36° = 72°

3 x = 3 ∙ 36° = 108°

The smaller angle is 72°

Let's call the two interior angles A and B. According to the given information, the ratio of angle A to angle B is 2:3.

To find the actual angle measures, we need to determine the value of the common ratio. Since the total ratio is 2:3, the sum of the ratios is 2 + 3 = 5.

To find the value of each ratio unit, we divide the total ratio by the sum of the ratios: 180 degrees (which is the sum of the two interior angles) divided by 5.

180 degrees ÷ 5 = 36 degrees

Now, we can calculate the measures of angles A and B:

Angle A = 2 * 36 degrees = 72 degrees
Angle B = 3 * 36 degrees = 108 degrees

The smaller angle is 72 degrees.

To find the smaller angle, we can set up an equation using the given ratio.

Let's assume that the two interior angles on the same side of the transversal are 2x and 3x, where x is a common factor.

According to the given information, these angles are in a ratio of 2:3. So, we have:

2x : 3x

To find the value of x, we can set up an equation based on the fact that the sum of the interior angles on the same side of a transversal intersecting two parallel lines is 180 degrees.

The equation will be:

2x + 3x = 180

5x = 180

Dividing both sides of the equation by 5, we get:

x = 36

Now, to find the smaller angle, substitute the value of x back into the equation:

2x = 2 * 36 = 72 degrees

Therefore, the smaller angle is 72 degrees.