Question

23. The three angles of a quadrilateral are 90°, 50° and 70°. Find the measure

of the fourth angle.​

Answer 1

Given :

• Measures of the three angles of quadrilateral :-
• First angle = 90°
• Second angle = 50°
• Third angle = 70°

To find :

• Measure of the fourth angle

Concept :

For finding the measure of the fourth angle of the quadrilateral. We will assume the fourth angle as any variable. Let it be x. So, by adding all the angles and keeping it equal to the sum of the interior angles of the quadrialteral we will get the value of x. The resultant value will be our required answer.

Formula to calculate sum of interior angles of any polygon :-

• Sum of interior angles of polygon = (2n - 4) × 90°

where,

• n = number of sides in the polygon

Solution :

A quadrilateral has 4 sides, 4 angles.

So, number of sides (n) = 4

Let the fourth angle of the quadrialteral be x.

→ 90° + 50° + 70° + x = (2n - 4) × 90°

→ 210° + x = ((2 × 4) - 4) × 90°

→ 210° + x = (8 - 4) × 90°

→ 210° + x = 4 × 90°

→ 210° + x = 360°

→ x = 360° - 210°

→ x = 150°

The value of x = 150°.

Therefore, the fourth angle of quadrialteral = 150°.

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Verification :-

For verifying the measure of the fourth angle of the quadrialteral add all the angles of quadrilateral if they sum upto 360° (sum of interior angles of quadrilateral) then the values are right.

• First angle = 90°
• Second angle = 50°
• Third angle = 70°
• Fourth angle = 150°

Their sum :-

→ 90° + 50° + 70° + 150°

→ 360°

Sum of interior angles of quadrilateral = 360°.

Hence, verified.

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Know More :-

A regular polygon has :-

• All its sides equal to each other.
• All its interior angles equal to each other.
• All its exterior angles equal to each other.

Some related formulae :-

• Each exterior angle of a regular polygon = 360°/n
•  Exterior angle + Interior angle = 180°

Answer 2

Answer :

150°

Explanation :

In a quadrilateral,

Three angles are 90°, 50°, and 70°.

Find the fourth angle.

Let's assume the fourth angle as $x$

We know that, The sum of all angles in a quadrilateral is equal to 360°. And this is known as the ‘angle sum property’

According to angle sum property,

$\implies {90}^{ \circ} + {50}^{ \circ} + {70}^{ \circ} + x= {360}^{ \circ}$

$\implies \: {210}^{ \circ} + x = {360}^{ \circ}$

$\implies \: x = {360}^{ \circ} - {210}^{ \circ}$

$\implies \: x = {150}^{ \circ}$

Hence, the fourth angle is 150°