Question

the measures of the angles of $\triangle abc$ are given by the expressions in the table.

angle	measure
b	$20^{circ}$
c	$(x + 14)^{circ}$

what are the measures of angles a and c?

enter your answers in the boxes.
$m\angle a=\square^{circ}$

Explanation:

Step1: Sum angles to 180°

$$(6x-1) + 20 + (x+14) = 180$$

Step2: Simplify the equation

$$7x + 33 = 180$$

Step3: Solve for x

$$7x = 180 - 33 = 147$$
$$x = \frac{147}{7} = 21$$

Step4: Calculate ∠A

$$m\angle A = 6(21) - 1 = 126 - 1 = 125$$

Step5: Calculate ∠C

$$m\angle C = 21 + 14 = 35$$

Answer:

$m\angle A = 125^\circ$
$m\angle C = 35^\circ$