Two supplementary angles are in the ratio 7:11. Find the measure of the smaller angle.
Two Angles are Supplementary if they add up to 180 °
A = smaller angle
B = larger angle
A / B = 7 / 11 Multiply both sides with 11
11 A / B = 7 Multiply both sides with B
11 A = 7 B Divide both sides with 11
A = ( 7 / 11 ) B
A + B = 180 °
( 7 / 11 ) B + B = 180 °
( 7 / 11 ) B + ( 11 / 11 ) B = 180°
( 18 / 11 ) B = 180 °
18 B = 180 ° * 11 Divide both sides with 18
18 B / 18 = 180 ° / 18 * 11
B = 10 ° * 11
B = 110 °
A = ( 7 / 11 ) B
A = ( 7 / 11 ) * 110
A = 770 / 11
A = 70 °
The smaller angle = 70 °
X equals 1 and so does any other letter of the alphabet like y,g,h, etc.
Nice anwser
What does X equal?
To find the measure of the smaller angle when two supplementary angles are given in a ratio, we can follow these steps:
Step 1: Set up the ratio equation:
Let the measures of the two angles be 7x and 11x, where x is the common factor for the ratio 7:11.
Step 2: Use the property of supplementary angles:
Since the two angles are supplementary, their sum is 180 degrees. So, we can write the equation:
7x + 11x = 180
Step 3: Simplify the equation:
Combine like terms:
18x = 180
Step 4: Solve for x:
Divide both sides of the equation by 18:
x = 180 / 18 = 10
Step 5: Find the measure of the smaller angle:
Substitute the value of x back into the expression for the smaller angle:
7x = 7 * 10 = 70
Therefore, the measure of the smaller angle is 70 degrees.