Question

please complete the chart with the correct angle measures. angle 43°, complement 51°, supplement 162°, vertical 13°

Explanation:

Step1: Recall angle - relationship formulas

Complementary angles add up to 90°. Supplementary angles add up to 180°. Vertical angles are equal.

Step2: Find the complement of 43°

Let the complement be \(x\). Then \(x + 43^{\circ}=90^{\circ}\), so \(x=90^{\circ}- 43^{\circ}=47^{\circ}\).

Step3: Find the complement of 51°

Let the complement be \(y\). Then \(y + 51^{\circ}=90^{\circ}\), so \(y = 90^{\circ}-51^{\circ}=39^{\circ}\).

Step4: Find the supplement of 162°

Let the supplement be \(z\). Then \(z+162^{\circ}=180^{\circ}\), so \(z = 180^{\circ}-162^{\circ}=18^{\circ}\).

Step5: Find the vertical - angle of 13°

Vertical angles are equal, so if one angle is 13°, its vertical - angle is also 13°.

Answer:

Angle	Complement	Supplement	Vertical
\(51^{\circ}\)	\(39^{\circ}\)	\(129^{\circ}\)	-
\(162^{\circ}\)	-	\(18^{\circ}\)	-
\(13^{\circ}\)	\(77^{\circ}\)	\(167^{\circ}\)	\(13^{\circ}\)