Question

complementary and supplementary angles
instruction active
calculating angle measures
what is the value of y?
y =
find the following angle measures.
m∠jkm =
°
m∠mkl =
°
$(10y + 6)^circ$
$(8y - 6)^circ$

Explanation:

Step1: Set up supplementary angle equation

The angles $\angle JKM$ and $\angle MKL$ form a straight line, so they are supplementary (sum to $180^\circ$):
$$(10y + 6) + (8y - 6) = 180$$

Step2: Simplify and solve for $y$

Combine like terms and isolate $y$:
$$18y = 180$$
$$y = \frac{180}{18} = 10$$

Step3: Calculate $m\angle JKM$

Substitute $y=10$ into the expression:
$$m\angle JKM = 10(10) + 6 = 106$$

Step4: Calculate $m\angle MKL$

Substitute $y=10$ into the expression:
$$m\angle MKL = 8(10) - 6 = 74$$

Answer:

$y = 10$
$m\angle JKM = 106^\circ$
$m\angle MKL = 74^\circ$