Solving Problems Involving Geometry

Two angles are supplementary if the sum of their measures is 180° Two angles are supplementary if the sum of their measures is 180°. The measure of the first angle is 42° less than four times the second angle. Find the measure of each angle. We’re asked to find the measure of two angles so, … Let F = the measure of the first angle Let S = the measure of the second angle

Our first equation is: F + S = 180 Now we need to find out two relationships between the first angle and the second angle. Two angles are supplementary if the sum of their measures is 180°. The first angle + the second angle = 180 Our first equation is: F + S = 180

Our second equation is F = 4S - 42 We need one more relationship between the first angle and the second angle. 2) The measure of the first angle is 42° less than four times the second angle. The measure of the first angle F is = 42° less than four times the second angle 4S – 42 NOTE: than reverses the order. The 42 came first in English and comes last in algebra. Our second equation is F = 4S - 42

Now we have two equations in two unknowns: F + S = 180 F = 4S – 42 I would solve these using substitution: 4S – 42 + S = 180 5S – 42 = 180 5S = 222 S = 44.4

Now let’s find the measure of the first angle and check our work: F = 4S – 42 S = 44.4 F = 4(44.4) – 42 F = 177.6 – 42 F = 135.6 Now we have that the first angle has a measure of 135.6 and the second angle has a measure of 44.4. Does that fit the story that they’re supplementary? 135.6 + 44.4 = 180 180 = 180 That works! The first angle is 135.6 and the second angle is 44.4