Question

complementary angles = 90 degrees. supplementary angles = 180 degrees.
9
read and solve
the problem below:
∠a is complementary
to ∠b and ∠b is
supplementary to ∠c.
if m∠a = (9x - 2)° and
m∠b = (5x + 8)°, find m∠c.
a) 52° doing sprints
b) 38° playing tubas
c) 136° watching jeopardy
d) 142° eating snow cones
e) 128° baking cupcakes

Explanation:

Step1: Use complementary angle rule

$m\angle A + m\angle B = 90^\circ$
Substitute the given expressions:
$(9x - 2) + (5x + 8) = 90$

Step2: Simplify and solve for $x$

Combine like terms:
$14x + 6 = 90$
Subtract 6 from both sides:
$14x = 84$
Divide by 14:
$x = \frac{84}{14} = 6$

Step3: Calculate $m\angle B$

Substitute $x=6$ into $m\angle B$:
$m\angle B = (5(6) + 8)^\circ = (30 + 8)^\circ = 38^\circ$

Step4: Use supplementary angle rule

$m\angle B + m\angle C = 180^\circ$
Solve for $m\angle C$:
$m\angle C = 180^\circ - m\angle B$

Step5: Compute final value

Substitute $m\angle B=38^\circ$:
$m\angle C = 180^\circ - 38^\circ = 142^\circ$

Answer:

D) $142^\circ$ eating snow cones