Question

choose all answers that describe the quadrilateral (abcd) if (mangle a = 90^circ), (mangle b = 78^circ), (mangle c = 49^circ), and (mangle d = 143^circ).

answer attempt 1 out of 10

• parallelogram
• quadrilateral
• rectangle
• rhombus
• square
• trapezoid

Explanation:

Step1: Verify quadrilateral angle sum

The sum of interior angles of a quadrilateral is $360^\circ$. Calculate the sum of given angles:
$$90^\circ + 78^\circ + 49^\circ + 143^\circ = 360^\circ$$

Step2: Check parallelogram criteria

Parallelograms have opposite angles equal. Here, $90^\circ
eq 49^\circ$ and $78^\circ
eq 143^\circ$, so it is not a parallelogram.

Step3: Check rectangle/rhombus/square criteria

Rectangles, rhombuses, and squares are all types of parallelograms. Since it is not a parallelogram, it cannot be any of these.

Step4: Check trapezoid criteria

A trapezoid has at least one pair of parallel sides (consecutive angles supplementary). Check consecutive angle sums:
$90^\circ+78^\circ=168^\circ
eq180^\circ$, $78^\circ+49^\circ=127^\circ
eq180^\circ$, $49^\circ+143^\circ=192^\circ
eq180^\circ$, $143^\circ+90^\circ=233^\circ
eq180^\circ$. No parallel sides, so not a trapezoid.

Step5: Confirm basic classification

Since the angle sum equals $360^\circ$, it is a quadrilateral.

Answer:

Quadrilateral