Question

Suppose that AKLM is isosceles with base MK.Suppose also that m ZM=(3x +36) and m ZK= (4x +31).Find the degree measure of each angle in the triangle.m ZK =m 2L =m 2M = 1MA(3x +36)(4x +31)Х?© 2021 McGraw-Hill Education. All Rights ReSearch for anythingOBI

Answer 1

Since we have an isosceles triangle, the opposite angles to the congruent sides are also congruent. That is, the measure of angle M and measure of angle K are congruent too.

Therefore, we have:

$3x+36=4x+31$

Now, we need to solve this equation for x, as follows:

1. Subtract 3x from both sides of the equation:

$3x-3x+36=4x-3x+31\Rightarrow36=x+31$

2. Subtract 31 from both sides of the equation:

$36-31=x+31-31\Rightarrow5=x\Rightarrow x=5$

Then, the value for x = 5.

To find the values for the angles, we need to substitute this value, x = 5, into the given expressions:

The measure of angle K$m\angle K=4x+31=4\cdot5+31=51\Rightarrow m\angle K=51$The measure of angle M

It is the same as the measure of angle K:

$m\angle M=3x+36=3\cdot5+36=15+36=51\Rightarrow m\angle M=51$The measure of angle L

The internal angles of a triangle sum up to 180 degrees. Therefore, we can find the measure of angle L as follows:

$m\angle M+m\angle K+m\angle L=180$

Then

$m\angle L=180-m\angle M-m\angle K\Rightarrow m\angle L=180-51-51=78$

Therefore, the measure of angle L is equal to 78 degrees.

In summary, we have that:

• m,• m,• m