Problem 9
Maxwell Lim
<JKL is congruent to <WXY. <JKL is supplementary to <LKM. m<WXY=4x+10 and m<JFK=5x-6. Find x, m<JKL and m<LKM
In order to find x you have to set up an equation for x.
m<JKL=5x-6 m<WXY=4x+10 Given
m<JKL=m<WXY Definition of Congruent Angles
5x-6=4x+10 Substitution Property
x-6=10 Subtraction Property
x=16 Addition Property
m<JKL=5x-6 m<WXY=4x+10 Given
m<JKL=m<WXY Definition of Congruent Angles
5x-6=4x+10 Substitution Property
x-6=10 Subtraction Property
x=16 Addition Property
Now that we have found x we need to input it into the equation
m<JKL=5x-6 m<WXY=4x+10 Given
m<JKL=m<WXY Definition of Congruent Angles
5x-6=4x+10 Substitution Property
5(16)-6=4(16)+10 Substitution Property
80-6=64+10 Distributive Property
74=74 Simplify
m<JKL=5x-6 m<WXY=4x+10 Given
m<JKL=m<WXY Definition of Congruent Angles
5x-6=4x+10 Substitution Property
5(16)-6=4(16)+10 Substitution Property
80-6=64+10 Distributive Property
74=74 Simplify
We found the measure of <JKL but we are not done since we still need to find the measure of <LKM
m<JKL=74 Given
m<JKL+m<LKM=180 Definition of supplementary angles
74+m<LKM=180 Substitution Property
m<LKM=106 Subtraction Property
m<JKL=74 Given
m<JKL+m<LKM=180 Definition of supplementary angles
74+m<LKM=180 Substitution Property
m<LKM=106 Subtraction Property
x=16 m<JKL=74 m<LKM=106