x = 17
m∠JKL = 87°
m∠KJL = 58°
m∠KLJ = 35°
m∠KLM = 145°
Step-by-step explanation:
The exterior angle theorem says that the sum of two interior angles is equal to the exterior angle
In the given triangle, the interior angles are:
m∠K = (7x-32)°
m∠J = (5x-27)°
The interior angle is:
m∠L = (9x-8)°
So writing mathematically
m∠J+m∠K = m∠L
[tex]7x-32+5x-27 = 9x-8\\12x -59 = 9x - 8\\12x-9x = 59-8\\3x = 51[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3} =\frac{51}{3}\\x = 17[/tex]
Now m∠JKL
= [tex]7x-32\\=7(17) - 32\\=119-32\\=87[/tex]
m∠KJL
[tex]= 5x-27\\=5(17)-27\\=85-27\\=58[/tex]
m∠KLJ
[tex]=188-9x\\=188-153\\=35[/tex]
m∠KLM
[tex]=9x-8\\=9(17) -8\\=153-8\\=145[/tex]
Hence,
x = 17
m∠JKL = 87°
m∠KJL = 58°
m∠KLJ = 35°
m∠KLM = 145°
Keywords: Angles, Triangle
Learn more about angles at:
- brainly.com/question/10772249
- brainly.com/question/10781917
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