Question

In Triangle JKL, angle K is 3 times the measure of angle J, and angle L is 8 times the measure of angle J. Find the measure of each angle in Triangle JKL.

Answer 1

The measures of angles J, K, and L in Triangle JKL are 15 degrees, 45 degrees, and 120 degrees respectively, calculated by using the fact that the sum of the angles in a triangle is 180 degrees.

Step-by-step explanation:

To solve for the measure of each angle in Triangle JKL where angle K is 3 times the measure of angle J, and angle L is 8 times the measure of angle J, we use the fact that the sum of the angles in any triangle is 180 degrees.

Let the measure of angle J be represented by 'x'. Thus, angle K will be '3x', and angle L will be '8x'. Setting up the equation, we have:

x + 3x + 8x = 180

Simplifying, we combine like terms:

12x = 180

Dividing both sides by 12 to solve for x, we get:

x = 15 degrees.

This means angle J is 15 degrees, angle K is 45 degrees (3 times 15), and angle L is 120 degrees (8 times 15).

Answer 2

Solution:
here, in triangle JKL, let angle J be x,
Then,
angle K = 3x
angle L = 8x

Now,
J + K + L = 180°
x + 3x + 8x = 180°
12x = 180°
x = 180°/12
x = 15°
So,
angle J = x
= 15°
angle K = 3x
= 3*15°
= 45°
angle L = 8x
= 8*15°
= 120°