In a parallelogram, opposite angles are equal. Therefore, m∠B = m∠C = 143° and m∠A = m∠D = 37°.
In parallelogram ABCD, opposite angles are equal, so mZC = mZA = 37°.
To find mZD, we can use the fact that the angles in a parallelogram add up to 360°. So, we have:
mZA + mZB + mZC + mZD = 360°
Substituting in the values we know, we have:
37° + 143° + 37° + mZD = 360°
Combining like terms, we have:
217° + mZD = 360°
Subtracting 217° from both sides, we have:
mZD = 360° - 217°
Therefore, mZD = 143°.
Explanation in detail:
A parallelogram is a quadrilateral with opposite sides parallel.
This means that opposite angles are equal, and opposite sides have the same length.
In parallelogram ABCD, we know that mZA = 37°.
Since opposite angles in a parallelogram are equal, mZC = mZA = 37°.
To find mZD, we can use the fact that the angles in a quadrilateral add up to 360°.
So, we have:
mZA + mZB + mZC + mZD = 360°
Substituting in the values we know, we have:
37° + 143° + 37° + mZD = 360°
Combining like terms, we have:
217° + mZD = 360°
Subtracting 217° from both sides, we have:
mZD = 360° - 217°
Therefore, mZD = 143°.