Question

If one of the angle measures more than ${{180}^{\circ }}$ in a quadrilateral then, that is known as
A. a parallelogram
B. a concave quadrilateral
C. a convex quadrilateral
D. a trapezium

Answer 1

Hint: To solve this question, consider all four options separately and then see which of the given type of quadrilateral has an angle more than ${{180}^{\circ }}$ this will make solution easy and understandable. We will try to analyze the angles of each 4 options quadrilateral and see which one of them have an angle greater than ${{180}^{\circ }}$

Complete step-by-step answer:
Consider option A a parallelogram. It looks like

ABCD is a parallelogram.
A parallelogram is a flat shaped with opposite sides parallel and equal in length. Also, opposite angle add to ${{180}^{\circ }}$ therefore, as angle add to give ${{180}^{\circ }}$ then, no angle of a parallelogram is more than ${{180}^{\circ }}$. Therefore option A is wrong.
Consider option B a concave quadrilateral.
A concave quadrilateral is a four sided polygon that has one interior angle that exceeds ${{180}^{\circ }}$ . It has one angle measure more than ${{180}^{\circ }}$ it looks like

So, option B is the correct answer.
Consider option C a convex quadrilateral.
A convex quadrilateral is a four sided polygon that has interior angles that measure less than ${{180}^{\circ }}$ . It has no side that measures more than ${{180}^{\circ }}$ it looks like

So option C is wrong.
Consider option D a trapezium.
A trapezium is a quadrilateral which has only one pair of parallel sides. It looks like

Usually it does not have any angle greater than ${{180}^{\circ }}$
So option D is wrong.
So, the correct answer is “Option B”.

Note: The key point in this question is that the students can get confused between convex quadrilateral and concave quadrilateral. Always remember, concave is a surface that curves inward therefore, it can have angle greater than ${{180}^{\circ }}$ and convex is curved outward so, it cannot have any angle greater than ${{180}^{\circ }}$