Question

29) The three angles of a
quadrilateral are 76 degree 54
degree and 108 degree then
the measure of 4th angle is​

Answer 1

AnswEr :-

• Fourth angle of the quadrilateral is 122°.

Given :-

• The three angles of a quadrilateral are 76°, 54° and 108°.

To Find :-

• Measure of the 4th angle.

SoluTion :-

Here,

three angles are 76°, 54° and 108°.

Let 4th angle be x

As we know that the sum of the all four angles of a quadrilateral is 360°.

According to question :-

76 + 54 + 108 + x = 360

→ 130 + 108 + x = 360

→ 238 + x = 360

→ x = 360 - 238

→ x = 122°

Hence, fourth angle of the quadrilateral is 122°.

_____________________

Answer 2

Answer :

➥ The fourth angle of the Quadrilateral = 122°

Given :

➤ The three angles of a quadrilateral = 76°, 54° and 108°

To Find :

➤ Fourth angle of a Quadrilateral = ?

Required Solution :

Before we start our solution, let's first know about Quadrilateral.

A Quadrilateral is a plane figure.

• A Quadrilateral has 4 sides or edges.
• A Quadrilateral has 4 corners or vertices.
• A Quadrilaterals will typically has shapes with four sides like rectangle, square, trapezoid.
• Sum of all angles of a quadrilateral is 360°.

✎ Let's solve this question...

❒ According to the given Question, given that The three angles of a quadrilateral = 76°, 54° and 108° that means first angle of a Quadrilateral is 76°, second angle of a Quadrilateral is 54° and third angle of a Quadrilateral is 108° and we need to find the fourth angle of a Quadrilateral.

Now, we have first angle, second angle and third angle of a Quadrilateral.

• First angle of a Quadrilateral (1st) = 76°
• Second angle of a Quadrilateral (2nd) = 54°
• Third angle of a Quadrilateral (3rd) = 108°

✒ To find the measure of fourth angle, First we will consider the fourth angle angle be x, Then, let's solve the solution on the basis of conditions given above.

Let ,

The fourth angle be "x"

As we know that

The sum of all angles of a Quadrilateral is 360°.

1st angle + 2nd angle + 3rd angle + 4th angle = 360°

⇛ 76 + 54 + 188 + x = 360

⇛ 130 + 108 + x = 360

⇛ 238 + x = 360

⇛ x + 238 = 360

⇛ x = 360 - 238

⇛ x = 122°

║Hence, the fourth angle of a Quadrilateral is 360°.║

$\:$

Verification :

Sum of all angles of a Quadrilateral = 360°

››› 76 + 54 + 108 + 122 = 360

››› 130 + 108 + 122 = 360

››› 238 + 122 = 360

››› 360 = 360

Hence Verified