Question

Check whether 101,62,89and 108degree​ ​could be the possible angles of
a quadrilateral.

Answer 1

Required Solution :

Clarification :

Here are given the angles of a quadrilateral that are 101°, 62° , 89° & 108°. We have to find is it possible angles to form a quadrilateral or not. So, by the angle sum property of the quadrilateral, we can check whether it could be possible angles of a quadrilateral or not.

• Angle sum property of the quadrilateral states that the sum of the angles of a quadrilateral is equivalent to 360°.

Direct Solution :

As we know that,

$\boxed{\star \: \: \pmb { \blue{Sum \: of \: the \: angles \: of \: quadrilateral = {360}^{\circ} }} }$

LHS : Sum of the angles of the quadrilateral :

→ 101° + 62° + 89° + 108°

$\: \: \tiny\fbox{1} \: \: \tiny\fbox{2} \\ \: \: \: \: \: \large \sf{ 101} \\ \: \: \: \: \: \: \: \large \sf62 \\ \: \: \: \: \: \: \: \large \sf89 \\ \: \purple + \: \: \large \sf108 \\ \: \: \: \: \: \: \: - - - - - \\ \: \: \: \: \: \: \sf \blue{360} \\ \: \: \: \: \: - - - - -$

→ 360°

RHS : 360°

→ 360°

LHS = RHS ,

Henceforth, it could be possible to form a quadrilateral having these angles.

_______________________________

More about quadrilaterals :

• A quadrilateral is called a shape having 4 sides, 4 angles & 4 vertices.

• There are many types of quadrilaterals , such as :

• Square : It is a quadrilateral in which all of its sides are equal. It has all angles of 90°.Its diagonals bisect each other at 90°. It is also a parallelogram.

• Parallelogram : A parallelogram have 2 pairs of parallel sides. Its opposite angles are equal.

• Trapezium : It is a quadrilateral having one pair of parallel sides.

• Rhombus : It is a quadrilateral in which all of its sides are equal. Its diagonals bisect each other. Measure of its diagonals are not equal. It is also a parallelogram.

Answer 2

Basic criteria for making any closed figure a quadrilateral is to check whether the sum of all angles of it is 360° or not.

In this case,

sum = 101° + 62° + 89° + 108°

⇒ sum = 360°.

∴ It is possible.

More:-

How can you say that sum of all angles of a quadrilateral is equal to 360°?

1) Draw a quadrilateral.

2) Draw any one of it's diagonal.

3) Now we know that sum of all angles of a triangle = 180°. Since there are 2 triangles, thus sum = 180° + 180° = 360°.

Hence, proved.