Question

on your own: pairs of angles
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(8x - 7)° (12x + 57)°
s p q
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1 2 3 4 5 6 7 8 next

Explanation:

Step1: Recognize straight angle sum

The three angles along line $SQ$ add to $180^\circ$, so:
$$(8x - 7) + (12x + 57) = 180$$

Step2: Simplify the equation

Combine like terms:
$$20x + 50 = 180$$

Step3: Solve for $x$

Subtract 50, then divide by 20:
$$20x = 130 \implies x = \frac{130}{20} = 6.5$$

Step4: Calculate the target angle

Substitute $x=6.5$ into $(8x-7)$:
$$8(6.5) - 7 = 52 - 7 = 45$$
(Note: If the question asks for the other angle, substitute into $12x+57$: $12(6.5)+57=78+57=135$, but the blank implies the smaller angle, $45^\circ$)

Answer:

$45$