Problem 6
Lynn Palmer
<XYC is congruent to <ZYD and and <XYZ is congruent to <CYD. <XYZ and <ZYD are supplementary.
m< XYC=2x-10 and m<CYD=5y+5. In addition, angle ZYD= 150. Find x and the measure of angle CYD.
First, we need to set up our equations. Our first equation can be written as 2x-10=150 because <ZYD= <XYC, therefore we can substitute in their values of 2x-10 (angle XYC) and 150 (angle ZYD). Our next equation can be written as 5y+5+150=180 because <XYZ+ <ZYD=180 so we can substitute their values of 5y+5 (<CYD) and 150 (<ZYD) to get 5y+5+150=180. First, we need to find the value of x, which we can get with our first equation.
Statement: Reason:
2x-10=150 Given
2x=160 Addition Property of Equality
x=80 Division Property of Equality
We now have the first part of our answer complete. Now we can move on to the second part of the question, which is finding the measure of angle CYD. To find this, we can use our second equation.
Statement: Reason:
5y+5+150=180 Given
5y+155=180 Simplify
5y=25 Subtraction Property of Equality
y=5 Division Property of Equality
Although we have found the y value, we have not finished the problem yet. We need to find the measure of <CYD, which means that we still have to plug y=5 into 5y+5.
5(5)+5
25+5=30
m<CYD=30
X=80 and m<CYD=30 degrees
m< XYC=2x-10 and m<CYD=5y+5. In addition, angle ZYD= 150. Find x and the measure of angle CYD.
First, we need to set up our equations. Our first equation can be written as 2x-10=150 because <ZYD= <XYC, therefore we can substitute in their values of 2x-10 (angle XYC) and 150 (angle ZYD). Our next equation can be written as 5y+5+150=180 because <XYZ+ <ZYD=180 so we can substitute their values of 5y+5 (<CYD) and 150 (<ZYD) to get 5y+5+150=180. First, we need to find the value of x, which we can get with our first equation.
Statement: Reason:
2x-10=150 Given
2x=160 Addition Property of Equality
x=80 Division Property of Equality
We now have the first part of our answer complete. Now we can move on to the second part of the question, which is finding the measure of angle CYD. To find this, we can use our second equation.
Statement: Reason:
5y+5+150=180 Given
5y+155=180 Simplify
5y=25 Subtraction Property of Equality
y=5 Division Property of Equality
Although we have found the y value, we have not finished the problem yet. We need to find the measure of <CYD, which means that we still have to plug y=5 into 5y+5.
5(5)+5
25+5=30
m<CYD=30
X=80 and m<CYD=30 degrees