Question

choose all answers that describe the quadrilateral bcde if m∠b = 150°, m∠c = 37°, m∠d = 117°, and m∠e = 56°. answer attempt 2 out of 2 parallelogram quadrilateral rectangle rhombus square trapezoid

Explanation:

Step1: Recall angle - sum property of quadrilaterals

The sum of interior angles of a quadrilateral is $(4 - 2)\times180^{\circ}=360^{\circ}$. Calculate the sum of the given angles: $150^{\circ}+37^{\circ}+117^{\circ}+56^{\circ}=360^{\circ}$, so it is a quadrilateral.

Step2: Recall properties of special quadrilaterals

• For a parallelogram, opposite angles are equal. Here, no two opposite - angle pairs are equal.
• For a rectangle, all angles are $90^{\circ}$. Here, none of the angles is $90^{\circ}$.
• For a rhombus, opposite angles are equal. Here, no two opposite - angle pairs are equal.
• For a square, all angles are $90^{\circ}$. Here, none of the angles is $90^{\circ}$.
• For a trapezoid, there is no information about parallel sides. But since it is a four - sided polygon, it is a quadrilateral.

Answer:

B. Quadrilateral