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.