Find the measure for angles y and z.
If angle x has a measure of 60° and the measure of angle y is 15° more than twice the measure of angle z. Write a system of equations and solve.
x = 60
y = 2z+15
Now, what did you forget to mention?
To solve for the measures of angles y and z, we can set up a system of equations based on the given information.
Let's represent the measure of angle z as "z" and the measure of angle y as "y".
The first equation we can write is:
y = 2z + 15
This equation states that the measure of angle y is 15° more than twice the measure of angle z.
The second equation we can write is:
x + y + z = 180
This equation states that the sum of the measures of angles x, y, and z in a triangle is 180°.
Now, we can substitute the value of x (60°) into the second equation:
60 + y + z = 180
Next, we substitute the value of y from the first equation into the second equation:
60 + (2z + 15) + z = 180
Now, we can simplify the equation:
60 + 2z + 15 + z = 180
3z + 75 = 180
Subtract 75 from both sides of the equation:
3z = 180 - 75
3z = 105
Divide both sides of the equation by 3:
z = 35
Now that we have found the value of z, we can substitute it back into the first equation to find y:
y = 2z + 15
y = 2(35) + 15
y = 70 + 15
y = 85
Therefore, the measure of angle y is 85° and the measure of angle z is 35°.