Question

find the measure of the missing angles.
answer
attempt 1 out of 3
g =
h =
k =
m =

Explanation:

Step1: Use the concept of supplementary angles

Supplementary angles add up to \(180^{\circ}\). For angle \(g\), \(g + 119^{\circ}=180^{\circ}\), so \(g = 180^{\circ}- 119^{\circ}=61^{\circ}\).

Step2: Use the property of vertical angles

Vertical angles are equal. Since \(h\) and \(119^{\circ}\) are supplementary (as in step 1) and also \(h\) and \(g\) are vertical angles (but we can also note that \(h\) and \(119^{\circ}\) form a linear - pair. Wait, no, actually \(h\) and \(119^{\circ}\) are adjacent and form a straight line. Wait, no, looking at the figure, \(h\) and \(119^{\circ}\) are adjacent and form a straight line (linear - pair). But also, for the lower part, for angle \(k\), \(k+121^{\circ}=180^{\circ}\), so \(k = 180^{\circ}-121^{\circ}=59^{\circ}\).

Step3: Use the property of vertical angles again

For angle \(m\), since \(m\) and \(k\) are supplementary ( \(m + k=180^{\circ}\), but also \(m\) and \(121^{\circ}\) are vertical angles. Wait, no. Using the linear - pair (supplementary) concept: \(m=180^{\circ}-121^{\circ}=59^{\circ}\) (because \(m\) and \(121^{\circ}\) form a linear - pair), and \(k\) (since \(k\) and \(121^{\circ}\) are supplementary \(k = 180 - 121=59^{\circ}\)), and \(h\) (since \(h\) and \(119^{\circ}\) are supplementary \(h=180 - 119 = 61^{\circ}\), and \(g\) ( \(g\) and \(119^{\circ}\) are supplementary \(g=61^{\circ}\))

Answer:

\(g = 61^{\circ}\), \(h = 61^{\circ}\), \(k = 59^{\circ}\), \(m = 59^{\circ}\)