Question

Please help me! 80 points!

Answer 1

• x = 17
• m∠JKL = 87°
• m∠KJL = 58°
• m∠KLJ = 35°
• m∠KLM = 145°

Explanation:

Since exterior angle of a triangle is equal to the sum of two interior opposite angles.

So,

m∠JKL + m∠KJL = m∠KLM

Substitute the given value:

(7x - 32)° + (5x -27)° = (9x - 8)°

7x -32 +5x -27 = 9x - 8

Simplify like terms:

12x - 59 = 9x - 8

Add 59 on both sides:

12x - 59 + 59 = 9x - 8 + 59

12x = 9x + 51

Subtract 9x on both sides:

12x - 9x = 9x + 51 - 9x

3x = 51

Divide both sides by 3.

`(3x)/(3)=(51)/(3)`

x = 17

Now

We can find the other angles by substitution value of x.

m∠JKL = (7×17 -32)° = (119 - 32)° = 87°

m∠KJL = (5 × 17 - 27)° = (85 - 27)° = 58°

m∠KLM = (9 × 17 - 8)° = (153 - 8)° = 145°

And Finally:

m∠KLJ and m∠KLM are linear pair and they are supplementary means added up to 180°

So,

m∠KLJ + m∠KLM = 180°

Substitute the known value:

m∠KLJ + 145° = 180°

Subtract 145° on both sides:

m∠KLJ + 145° - 145° = 180° - 145°

m∠KLJ = 35°

Summary:

• x = 17
• m∠JKL = 87°
• m∠KJL = 58°
• m∠KLJ = 35°
• m∠KLM = 145°