Question

L and M are complementary, L = 2x + 25, and M = 4x + 11. Determine the measure of each angle.

Answer 1

Answer:

$L = 43$    and   $M = 47$

Step-by-step explanation:

Given

$L = 2x + 25$

$M = 4x + 11$

Required

Determine the values of L and M

Since L and M are complementary, we have that

$L + M = 90$

Substitute values for L and M

$2x + 25 + 4x + 11 = 90$

Collect Like Terms

$2x + 4x = 90 - 11 - 25$

$6x = 54$

Divide both sides by 6

$x = \frac{54}{6}$

$x = 9$

Substitute 9 for x in the expressions of L and M

$L = 2x + 25$

$L = 2 * 9 + 25$

$L = 18 + 25$

$L = 43$

$M = 4x + 11$

$M = 4 * 9 + 11$

$M = 36 + 11$

$M = 47$