Question

The measure of angle JKL can be represented using the expression 3x + 5.

What is the degree measure of JKL?

Answer 1

The measure of ∠JKL is 65°

Explanation:

Consider the provided diagram.

We need to find the degree measure of ∠JKL.

It is given that ∠JKM=45° and ∠MKL=x°

Also it is given that the measure of angle JKL can be represented using the expression 3x + 5.

Thus ∠JKL=3x+5

From the figure it can be concluded that ∠JKL is equal to the sum of ∠JKM and ∠MKL

This can be written as:

∠JKL = ∠JKM+∠MKL

Substitute the respective values in the above equation.

3x+5 = 45+x

Subtract x and 5 from both the sides.

3x+5-x-5 = 45+x-x-5

2x = 40

x = 20

Thus, the measure of ∠MKL=20°

Substitute the value of x in ∠JKL = 3x+5.

∠JKL = 3(20)+5

∠JKL = 60+5

∠JKL = 65

Hence, the measure of ∠JKL is 65°

Answer 2

∠JKL = 65°

Explanation:

We are given that:

∠JKL = 3x + 5

∠JKM = 45°

∠MKL = x°

Now, we know that ∠JKL is the summation of ∠JKM and ∠MKL

Therefore:

∠JKL = ∠JKM + ∠MKL

Substitute with the givens in the above equation and solve for x:

∠JKL = ∠JKM + ∠MKL

3x + 5 = 45° + x

3x - x = 45 - 5

2x = 40

x = 20

This means that:

∠JKL = 3x + 5 = 3(20) + 5 = 65°

∠JKM = 45°

∠MKL = x° = 20°

Check:

∠JKL = ∠JKM + ∠MKL

∠JKL = 45° + 20° = 65° ..........> verified

Hope this helps :)