Question

In ΔIJK, I K ‾ IK is extended through point K to point L, m ∠ J K L = ( 5 x − 3 ) ∘ m∠JKL=(5x−3) ∘ , m ∠ K I J = ( 2 x + 8 ) ∘ m∠KIJ=(2x+8) ∘ , and m ∠ I J K = ( x − 1 ) ∘ m∠IJK=(x−1) ∘ . Find m ∠ J K L . M∠JKL.

Answer 1

22 degrees.

Explanation:

From the given question we are given the following:

Exterior angle m ∠ J K L = ( 5 x − 3 )°

Interior angles;

m∠KIJ=(2x+8)°

m∠IJK=(x−1)°

Note that the sum of interior angles is equal to the exterior angles;

Hence, m∠KIJ +m∠IJK = m∠JKL

Substitute the given values;

2x+8 + x -1 = 5x - 3

3x + 7 = 5x - 3

Collect like terms;

3x - 5x = -3-7

-2x = -10

x = 10/2

x = 5

Get m∠JKL

m∠JKL = 5x - 3

m∠JKL= 5(5)-3

m∠JKL = 25-3

m∠JKL = 22°

hence the measure of m∠JKL is 22 degrees.