One angle of a parallelogram measures 40°. What are the measures of the other three angles in the parallelogram? _____°, _____°, and _____°

Identify Opposite Angles: One angle of a parallelogram measures 40°. We know that in a parallelogram, opposite angles are equal. Therefore, the angle opposite to the 40° angle will also measure 40°.Calculate Sum of Remaining Angles: Next, we need to find the measure of the adjacent angles. Since the angles in a parallelogram add up to 360°, and we have two angles that are 40° each, we can calculate the sum of the remaining two angles. Sum of the remaining two angles = 360° - (40° + 40°) = 360° - 80° = 280°.Find Measure of Adjacent Angles: Since the remaining two angles are also opposite each other, they must be equal. Therefore, each of these angles measures half of 280°. Measure of each of the remaining angles = 280° / 2 = 140°.

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One angle of a parallelogram measures $40^\circ$ . What are the measures of the other three angles in the parallelogram? $\newline$ $\underline{\hspace{1cm}}^\circ,$ $\underline{\hspace{1cm}}^\circ,$ and $\underline{\hspace{1cm}}^\circ$

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Math Problems

Grade 8

Find missing angles in quadrilaterals II

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Q. One angle of a parallelogram measures

40^\circ

. What are the measures of the other three angles in the parallelogram?

\newline

\underline{\hspace{1cm}}^\circ,

\underline{\hspace{1cm}}^\circ,

and

\underline{\hspace{1cm}}^\circ

Identify Opposite Angles: One angle of a parallelogram measures $40^\circ$ . We know that in a parallelogram, opposite angles are equal. Therefore, the angle opposite to the $40^\circ$ angle will also measure $40^\circ$ .
Calculate Sum of Remaining Angles: Next, we need to find the measure of the adjacent angles. Since the angles in a parallelogram add up to $360°$ , and we have two angles that are $40°$ each, we can calculate the sum of the remaining two angles. $\newline$ Sum of the remaining two angles = $360° - (40° + 40°) = 360° - 80° = 280°$ .
Find Measure of Adjacent Angles: Since the remaining two angles are also opposite each other, they must be equal. Therefore, each of these angles measures half of $280^\circ$ . $\newline$ Measure of each of the remaining angles = $280^\circ / 2 = 140^\circ$ .