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One angle of a parallelogram measures 40∘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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Q. One angle of a parallelogram measures 40∘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
  1. Identify Opposite Angles: One angle of a parallelogram measures 40∘40^\circ. We know that in a parallelogram, opposite angles are equal. Therefore, the angle opposite to the 40∘40^\circ angle will also measure 40∘40^\circ.
  2. 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°360°, and we have two angles that are 40°40° each, we can calculate the sum of the remaining two angles.\newlineSum of the remaining two angles = 360°−(40°+40°)=360°−80°=280°360° - (40° + 40°) = 360° - 80° = 280°.
  3. 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∘280^\circ.\newlineMeasure of each of the remaining angles = 280∘/2=140∘280^\circ / 2 = 140^\circ.

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