Question

If m∠JKM = 43, m∠MKL = (8 - 20), and m∠JKL = (10x - 11), find each measure.




1. x = ?

2. m∠MKL = ?

3. m∠DEF = ?​

Answer 1

Correct Question: If m∠JKM = 43, m∠MKL = (8x - 20), and m∠JKL = (10x - 11), find each measure.

1. x = ?

2. m∠MKL = ?

3. m∠JKL = ?

Answer/Step-by-step explanation:

Given:

m<JKM = 43,

m<MKL = (8x - 20),

m<JKL = (10x - 11).

Required:

1. Value of x

2. m<MKL

3. m<JKL

Solution:

1. Value of x:

m<JKL = m<MKL + m<JKM (angle addition postulate)

Therefore:

$(10x - 11) = (8x - 20) + 43$

Solve for x

$10x - 11 = 8x - 20 + 43$

$10x - 11 = 8x + 23$

Subtract 8x from both sides

$10x - 11 - 8x = 8x + 23 - 8x$

$2x - 11 = 23$

Add 11 to both sides

$2x - 11 + 11 = 23 + 11$

$2x = 34$

Divide both sides by 2

$\frac{2x}{2} = \frac{34}{2}$

$x = 17$

2. m<MKL = 8x - 20

Plug in the value of x

m<MKL = 8(17) - 20 = 136 - 20 = 116°

3. m<JKL = 10x - 11

m<JKL = 10(17) - 11 = 170 - 11 = 159°