The measures of the twoa angles in a linear pair are in the ratio 1:3. What is the measure of the lager angle?

L = Large angle

S = Smaller angle

S = L / 3

S + L = 180°

L / 3 + L = 180°

L / 3 + 3 L / 3 = 180°

4 L / 3 = 180°

4 L = 3 ∙ 180° = 540°

L = 540° / 4 =135°

S = L / 3 = 135° / 3 = 45°

Large angle = 135°

To find the measure of the larger angle in a linear pair, you first need to understand what a linear pair is.

A linear pair consists of two adjacent angles, formed by two intersecting lines. These angles share a common vertex and a common side, making them consecutive angles. The sum of the measures of the angles in a linear pair is always 180 degrees.

In this case, let's denote the measures of the two angles as 'x' and '3x' (since they are in the ratio 1:3).

According to the information given, we know that the sum of these two angles is 180 degrees:

x + 3x = 180

Combining like terms, we get:

4x = 180

To solve for 'x', divide both sides of the equation by 4:

x = 180 / 4
x = 45

Now that we have the value of 'x', we can find the measure of the larger angle by substituting this value back into the equation:

3x = 3 * 45
3x = 135

Therefore, the measure of the larger angle is 135 degrees.