Question

1. what is the sum of f° + g°?

(there is a diagram with angles labeled 60°, 50°, and angles a°, c°, d°, e°, f°, g°, i°, k°)

options:
360°
110°
180°
120°

Explanation:

Step1: Identify co-interior angles

First, we use the property of parallel lines: co-interior angles sum to $180^\circ$. For the left side, $60^\circ + g^\circ = 180^\circ$, so $g^\circ = 180^\circ - 60^\circ = 120^\circ$. For the right side, $50^\circ + e^\circ = 180^\circ$, so $e^\circ = 180^\circ - 50^\circ = 130^\circ$.

Step2: Sum quadrilateral interior angles

The figure forms a quadrilateral with angles $60^\circ, e^\circ, 50^\circ, g^\circ$? No, correct: the quadrilateral has angles $c^\circ, d^\circ, g^\circ, (180^\circ - 50^\circ)$? No, better: use the fact that for the two parallel lines, the sum of angles around the transversals: the sum of $f^\circ + g^\circ$ can be found by noting that $f^\circ = 180^\circ - g^\circ$? No, wait: $f^\circ + g^\circ$ is a straight line? No, no—wait, the sum of the exterior angles related to the parallel lines: the sum of $f^\circ + g^\circ$ is equal to $180^\circ + (60^\circ + 50^\circ) - 180^\circ$? No, correct method: use the property that the sum of the angles $f^\circ + g^\circ$ is equal to $180^\circ + 60^\circ - 50^\circ$? No, wait, the sum of the angles between parallel lines: the sum of $f^\circ + g^\circ$ is equal to $60^\circ + 50^\circ + 180^\circ - 180^\circ$? No, let's use the polygon angle sum. The quadrilateral has interior angles $60^\circ, (180^\circ - d^\circ), 50^\circ, (180^\circ - f^\circ)$? No, simpler: $f^\circ + g^\circ = 180^\circ + (60^\circ + 50^\circ) - 180^\circ$? No, wait, $g^\circ$ is supplementary to $60^\circ$? No, $g^\circ + 60^\circ +$ the other two angles in the quadrilateral sum to $360^\circ$. The other two angles are $e^\circ = 130^\circ$ and $d^\circ = 180^\circ - e^\circ$? No, $d^\circ + e^\circ = 180^\circ$, so $d^\circ = 50^\circ$. Then the quadrilateral angles are $60^\circ, d^\circ=50^\circ, 50^\circ, g^\circ$? No, that sums to $60+50+50+g=360$, so $g=200$, which is wrong. Oh! I made a mistake: $f^\circ + g^\circ$ is a straight line? No, no—$f^\circ$ and $g^\circ$ are adjacent angles forming a linear pair? No, no, the figure shows $f^\circ$ and $g^\circ$ are on a straight line, so $f^\circ + g^\circ = 180^\circ$? No, that's not an option. Wait, no! The question is sum of $f^\circ + g^\circ$? Wait no, the options include 110. Oh! I misread: $f^\circ$ is the exterior angle, $g^\circ$ is the interior angle. Wait, no: the sum of $f^\circ + g^\circ$ is equal to $180^\circ + 60^\circ - 50^\circ$? No, use the property that the sum of the exterior angles related to the parallel lines: $f^\circ = 50^\circ$, $g^\circ = 60^\circ$, so $f+g=110^\circ$. Yes! Because $f^\circ$ is equal to $50^\circ$ (corresponding angles), $g^\circ$ is equal to $60^\circ$ (corresponding angles), so $50+60=110$.

Step3: Calculate final sum

$f^\circ + g^\circ = 60^\circ + 50^\circ = 110^\circ$

Wait, correct step-by-step:

Step1: Use corresponding angles

$f^\circ = 50^\circ$ (corresponding angles for parallel lines)
$g^\circ = 60^\circ$ (corresponding angles for parallel lines)

Step2: Sum the two angles

$f^\circ + g^\circ = 50^\circ + 60^\circ = 110^\circ$

Yes, that's correct. Because $f^\circ$ corresponds to the $50^\circ$ angle, $g^\circ$ corresponds to the $60^\circ$ angle, so their sum is 110.

Step1: Identify corresponding angles

$f^\circ = 50^\circ$, $g^\circ = 60^\circ$

Step2: Sum the two angles

$f^\circ + g^\circ = 50^\circ + 60^\circ = 110^\circ$

Answer:

110°