Answer:
a. equation: 5x + x - 6 = 180, x=31
b. m<1=155°, m<2=25°
Explanation:
We are given a straight angle (due to the straight line given in the picture), which is intersected by a ray to create <1 and <2.
We are also given that m<1 = 5x and m<2=x-6, and we want to solve for x and find the measures of <1 and <2.
Part a:
Due to angle addition postulate, the measures of <1 and <2 will be equal to the measure of the straight angle.
A straight angle always is equal to 180°.
Based on this information, we can create this equation:
m<1 + m<2 = 180
Now, substitute the values of <1 and <2 into the equation to help solve it.
5x + x - 6 = 180
Combine the x's.
6x - 6 = 180
Add 6 to both sides.
6x = 186
Divide both sides by 6.
x = 31
The value of x is equal to 31.
Part b:
Now that we know the value of x, we can substitute that value to find the measures of <1 and <2.
As we were already given, m<1 = 5x, and since we now know the value of x, we can substitute this value as x.
m<1 = 5x
m<1=5*31
m<1=155°
The same can be said for m<2.
m<2 = x - 6
m<2 = 31 - 6
m<2 = 25°