Question

Choose ALL answers that describe the quadrilateral N, O, P, QNOPQ if m, angle, N, equals, 45, degreesm∠N=45 ∘ , m, angle, O, equals, 154, degreesm∠O=154 ∘ , m, angle, P, equals, 60, degreesm∠P=60 ∘ , and m, angle, Q, equals, 101, degreesm∠Q=101 ∘ .

Parallelogram
Quadrilateral
Rectangle
Rhombus
Square
Trapezoid

Answer 1

Using the given angle measures, we confirm that NOPQ is a quadrilateral as the angles sum up to 360 degrees. However, it doesn't meet the criteria for being a parallelogram, rectangle, rhombus, square, or trapezoid.

Step-by-step explanation:

To determine which descriptions apply to the quadrilateral NOPQ with given angle measures, we can use our knowledge of the properties of quadrilaterals and their angles. The sum of the angles in any quadrilateral is 360 degrees. If we add up the given angles of NOPQ:

m∠N (45 degrees) + m∠O (154 degrees) + m∠P (60 degrees) + m∠Q (101 degrees) = 360 degrees,

this confirms that NOPQ is indeed a quadrilateral.

Quadrilateral NOPQ has angles that do not meet the criteria for a parallelogram, rectangle, square, or rhombus, as these all require pairs of equal and parallel opposite sides, which is not indicated by the angle measures provided.

Also, based on the angle measures, NOPQ cannot be a trapezoid, which has only one pair of parallel sides. Therefore, the only description that certainly applies is that NOPQ is a quadrilateral.