Question

1. ∠a and ∠b are supplementary. if m∠a = (5x − 1)°, and m∠b = (5x + 21)°, solve for x and find m∠a and

x = ______
m∠a = ______
m∠b = ______

Explanation:

Step1: Set up supplementary angle equation

Supplementary angles sum to $180^\circ$, so:
$$(5x - 1) + (5x + 21) = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$10x + 20 = 180$$
$$10x = 160$$
$$x = 16$$

Step3: Calculate $m\angle A$

Substitute $x=16$ into $\angle A$'s expression:
$$m\angle A = 5(16) - 1 = 80 - 1 = 79$$

Step4: Calculate $m\angle B$

Substitute $x=16$ into $\angle B$'s expression:
$$m\angle B = 5(16) + 21 = 80 + 21 = 101$$

Answer:

$x = 16$
$m\angle A = 79^\circ$
$m\angle B = 101^\circ$