Question

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3. If three angles of a trapezium are 60°, 60° and 1200, find
the fourth angle.​

Answer 1

Correct Question :

If three angles of a trapezium are 60°, 60° and 120°, find the fourth angle.

Answer :

• The fourth angle = 120°.

Given :

The three angles of a trapezium :-

• First angle = 60°
• Second angle = 60°
• Third angle = 120°

To Find :

• The fourth angle.

Solution :

Let,

The fourth angle be x.

We know that,

Sum of all the angles of a trapezium is 360°

That means,

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

Where,

The three angles are given,

• 1st angle = 60°
• 2nd angle = 60°
• 3rd angle = 120°

⇒ 60° + 60° + 120° + x = 360°

⇒ 120° + 120° + x = 360°

⇒ 240° + x = 360°

⇒ x = 360° - 240°

⇒ x = 120°

Therefore,

⇒ x = 120°

Hence,

The fourth angle of a trapezium is 120°

Verification :

Sum of all the angles of a trapezium is 360°

That means,

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

Where,

The three angles are given,

• 1st angle = 60°
• 2nd angle = 60°
• 3rd angle = 120°
• 4th angle = 120°

⇒ 60° + 60° + 120° + 120° = 360°

⇒ 120° + 240° = 360°

⇒ 360° = 360°

Hence Verified !

Answer 2

Diagram:-

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Given:-

Three angles of a trapezium are 60°,60°,120°

To find:-

The fourth angle

Solution:-

Let the fourth angle=x

• We know that:-
• Trapezium is also a Quadiratral.
• In a Quadiratral sum of all four angles=360°

Thus

${\boxed{\sf The\:sum\:of\:angles=360°}}$

• Substitute the values

$\qquad\quad{:}\longrightarrow\sf 60+60+120+x=360$

• Simplify

$\qquad\quad{:}\longrightarrow\sf 120+120+x=360$

$\qquad\quad{:}\longrightarrow\sf 240+x=360$

$\qquad\quad{:}\longrightarrow\sf x=360-240$

$\qquad\quad{:}\longrightarrow\sf x=120°$

$\therefore\sf Measure\:of\:fourth\:angle\:is\;120°$

Verification :-

• We have to prove that the sum of angles =360

$\qquad\quad{:}\longrightarrow\sf 60+60+120+120=360$

$\qquad\quad{:}\longrightarrow\sf 120+240=360$

$\qquad\quad{:}\longrightarrow\sf 360=360$

$\therefore \underline{\sf Hence\:Verified.}$