Question

In AJKL, if m∠J is seven less than m∠L and m∠K is 21 less than twice m∠L, find the measure of each angle. m∠J = m∠K = m∠L =

a) 28°
b) 35°
c) 14°
d) 7°

Answer 1

In order to find the measure of each angle, we can set up equations for each angle and solve for their measures. By using the fact that the sum of angles in a quadrilateral is 360°, we can then determine the measure of each angle in the given quadrilateral.

Step-by-step explanation:

Given that m∠J is seven less than m∠L and m∠K is 21 less than twice m∠L, we can set up an equation for each angle.

Let's say m∠L = x. Then, m∠J = x - 7 and m∠K = 2x - 21.

We know that the sum of the angles in a quadrilateral is 360°. So, we have:

x + x - 7 + 2x - 21 + x = 360

Combining like terms, we get:
5x - 28 = 360
5x = 388
x = 77.6

Therefore, m∠J = 77.6 - 7 = 70.6°, m∠K = 2(77.6) - 21 = 134.2°, and m∠L = 77.6°.