Question

the angle of quadrilateral are in the ratio 7 :3:6:15 find all the anglea of the quadrilateral​

Answer 1

$\huge\bf{Answer :}$

Therefore, The Angles are $\huge\bf{81, 35, 70 \: and \: 174}$

$\huge\bf{Explanation :}$

Let,

The Angle of the quadrilateral be

$7x</em></strong><strong><em>,</em></strong><strong><em> </em></strong><strong><em>3x</em></strong><strong><em>,</em></strong><strong><em> </em></strong><strong><em>6x</em></strong><strong><em> </em></strong><strong><em>\</em></strong><strong><em>:</em></strong><strong><em> </em></strong><strong><em>and</em></strong><strong><em> </em></strong><strong><em>\</em></strong><strong><em>:</em></strong><strong><em> </em></strong><strong><em>15x$

All Angles of a quadrilateral measures a sum of 360°

Therefore,

$7x + 3x + 6x + 15x = 360 \\ 31x = 360 \\ x = \frac{360}{31} \\ x = 11.6$

So, The Angles are

• $7x = 7 \times 11.6 = 81$
• $3x =3 \times 11.6 = 35$
• $6x =6 \times 11.6 = 70$
• $15x =15 \times 11.6= 174$

Hence, The Angles are $81.35.70 \: and \: 174$

Answer 2

Answer :

›»› The all angles of the quadrilateral is

Given :

• The angle of quadrilateral are in the ratio 7:3:6:15.

To Find :

• The all angles of the quadrilateral = ?

Solution :

Let,

The angles of the quadrilateral be "7x", "3x", "6x", and "15x"

As we know that

The sum of all four angles of the quadrilateral is 360°.

→ 7x + 3x + 6x + 15x = 360

→ 10x + 6x + 15x = 360

→ 16x + 15x = 360

→ 31x = 360

→ x = 360/31

→ x = 11.61

Therefore,

→ The first angle = 7x

→ The first angle = 7 * 11.61

→ The first angle = 81°

→ The second angle = 3x

→ The second angle = 3 * 11.61

→ The second angle = 35°

→ The third angle = 6x

→ The third angle = 6 * 11.61

→ The third angle = 70°

→ The fourth angle = 15x

→ The fourth angle = 15 * 11.61

→ The fourth angle = 174°

║Hence, the all angles of the quadrilateral are 81°, 35°, 70°, and 174°.║

Verification :

The sum of all four angles of the quadrilateral is 360°.

→ 81 + 35 + 70 + 174 = 360

→ 116 + 70 + 174 = 360

→ 186 + 174 = 360

→ 360 = 360

Here, LHS = RHS

Hence Verified !