if two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3,then the smaller of two angles is
A = 2x.
B = 3x.
A + B = 180 deg.
2x + 3x = 180,
5x = 180,
x = 36,
2x = 2*36 = 72 = A = Smaller angle.
To find the measure of the smaller interior angle, we need to establish a relationship between the angles formed by the transversal intersecting two parallel lines.
Let's denote the smaller interior angle as x and the larger interior angle as y.
According to the given information, the ratio of the two interior angles is 2:3. This means that the smaller angle is 2 parts and the larger angle is 3 parts.
We can set up an equation using the given ratio:
x/y = 2/3
To find the value of x, we can cross-multiply:
3x = 2y
Next, we want to solve for x in terms of y. We can divide both sides of the equation by 3:
x = (2/3)y
This equation represents the relationship between the smaller angle (x) and the larger angle (y). It shows that the measure of the smaller angle is (2/3) times the measure of the larger angle.
Therefore, the smaller angle is (2/3) of the larger angle.