Question

EXERCISE 12
The three anglesola quadrilateral are 65 55° and 130°. Find its fiurth angel​

Answer 1

Question :-

The three angles of a quadrilateral are 65°, 55° and 130°. Find the fourth angle.

Answer :-

• The fourth angle of the quadrilateral is 110°.

Given :-

• The three angles of a quadrilateral are 65°, 55° and 130°.

To find :-

• The fourth angle of the quadrilateral.

Step-by-step explanation :-

We know the value of the three angles of a quadrilateral. We have to find the fourth angle.

We know that :-

Sum of all the angles in a quadrilateral = 360°.

So, clearly all these angles will add up to 360°.

Now, let the unknown angle be x°.

Therefore, we get :-

$\sf x^{\circ} + 65^{\circ} + 55^{\circ} + 130^{\circ} = 360^{\circ}$

Adding all the numbers,

$\sf x^{\circ} + 250^{\circ} = 360^{\circ}$

Transposing 250° from LHS to RHS, changing it's sign,

$\sf x^{\circ} = 360^{\circ} - 250^{\circ}$

Subtracting the numbers,

$\sf x^{\circ} = 110^{\circ}.$

The value of x° = 110°.

So, the fourth angle of the quadrilateral = 110°.