Question

Three angles of a quadrilateral are 60°, 86° and 110°. The fourth angle is

(a) 104° (b) 124° (c) 94° (d) 84°​

Answer 1

Quadrilateral

Let's know about the quadrilateral, before going to the solution directly.

• 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 equal to 360 degrees.

Let's understand the problem.

This question says us to find out the measure of the fourth angle of a quadrilateral, and we are given with the three angles of a quadrilateral, so by using the angle sum property of a quadrilateral we can easily find out the measure of the fourth angle of a quadrilateral.

Let's solve the problem now.

We've been given that three angles of the quadrilateral, i.e. $60^\circ$, $86^\circ$ and $110^\circ$. With this information, we've been asked to find out the fourth angle of the quadrilateral.

Let us consider that $a$ be the fourth angle of the quadrilateral.

We know that, The sum of interior angles of quadrilaterals is equal to 360 degrees. This statement is known as "Angle sum property of Quadrilateral". Therefore,

$\implies 60 + 86 + 110 + a = 360 \\ \\ \implies 146 + 110 + a = 360 \\ \\ \implies 256 + a = 360 \\ \\ \implies a = 360 - 256 \\ \\ \implies \boxed{a = 104}$

Therefore, the fourth angle of the quadrilateral is 104 degree. So, option (a) 104° is correct.

Answer 2

Answer:

Question :-

✯ Three angles of a quadrilateral are 60°, 86° and 110°. The fourth angle is

Options :

☯ (a) 104°

☯ (b) 124°

☯ (c) 94°

☯ (d) 84°

Given :-

✯ Three angles of a quadrilateral are 60°, 86° and 110°.

Find Out :-

✯ What is the fourth angle of a quadrilateral.

Solution :-

☣ Fourth angle of a quadrilateral :-

As we know that :

$\red{ \boxed{\sf{\bigstar\: Sum\: of\: all\: the\: four\: angles_{(Quadrilateral)} =\: 360^{\circ}\: \bigstar}}}$

Let, the fourth angle of a quadrilateral be x.

So, according to the question or ATQ :-

$\leadsto \tt{60^{\circ} + 86^{\circ} + 1100^{\circ} + x =\: 360^{\circ}}$

$\leadsto \tt{146^{\circ} + 1100^{\circ} + x =\: 360^{\circ}}$

$\leadsto \tt{256^{\circ} + x =\: 360^{\circ}}$

$\leadsto \tt{x =\: 360^{\circ} - 256^{\circ}}$

$\leadsto \tt{x =\: 104^{\circ}}$

$\leadsto$ ${\small{\bold{\purple{\underline{x =\: 104^{\circ}}}}}}$

Henceforth, the fourth angle of a quadrilateral is 104° .

Correct options is (a) 104° .

$\purple{\rule{45pt}{7pt}}\red{\rule{45pt}{7pt}}\pink{\rule{45pt}{7pt}}\blue{\rule{45pt}{7pt}}$

$\qquad\qquad\underline{\textsf{\textbf{ \color{magenta}{Brainly\: Extra\: Shots :-} }}}$

✈ Quadrilateral :

• A quadrilateral is a polygon with four sides.

✈ Properties of Quadrilateral :-

• Sum of the angles of a quadrilateral is 360°.
• Every quadrilateral has four sides.
• Every quadrilateral consist of four corners or vertex.
• A quadrilateral has 4 sides, 4 angles and 4 vertices.