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