Question

A student was asked to find m<1 and m<2 given that m<4 = 126º, m<1 = (9x - 16), and m<2 = (10x - 10). She incorrectly said m<1 = 22° and m<2 = 32º. Find m<1 and m<2. What mistake might the student have made?

Answer 1

To find m1 and m2, we can use the given information to solve for x and then substitute that value into the equations for m1 and m2.

Step-by-step explanation:

To find m1 and m2, we need to use the given information:

The student was asked to calculate m<1 and m<2 given that m<4 = 126º, m<1 = (9x - 16), and m<2 = (10x - 10). The correct way to solve for the angles is to use the information that the angles are likely related in some geometrical way, such as being supplementary angles if m<1 and m<2 add up to m<4 (as may be the case in a triangle or linear pair). Without more geometric context, we would need additional information to find the exact values of m<1 and m<2. Nevertheless, we can still identify the mistake made by the student.

m4 = 126º

m1 = 9x - 16

m2 = 10x - 10

Substitute m4 into the equation for m1:

126 = 9x - 16

9x = 142

x = 142/9

x ≈ 15.78

Now, substitute x ≈ 15.78 into the equation for m1:

m1 = 9(15.78) - 16

m1 ≈ 134.02º

Similarly, substitute x ≈ 15.78 into the equation for m2:

m2 = 10(15.78) - 10

m2 ≈ 147.8º

So, m1 ≈ 134.02º and m2 ≈ 147.8º.