Question

If the internal angles of the quadrilateral are in the ratio 6 : 5 : 8 : 5, what are the measures of its angles?
(a) 90°,74°,120°,76°
(b) 100°,75°,120°,75°
(c) 90°,75°,120°,75°
(d) 100°,75°,120°,75°​

Answer 1

• (c) Option is correct beacuse angles of quadrilateral are 90°, 75°, 120° and 75°.

Step-by-step explanation:

Given:-

• Ratio of interior angles of the quadrilateral is 6:5:8:5.

To find:-

• Measure of all angles.

Solution:-

Let, Angles of the quadrilateral be 6x, 5x, 8x and 5x.

We know that,

Sum of all interior angles of quadrilateral is 360°.

So,

➝ 6x + 5x + 8x + 5x = 360°

➝ 24x = 360°

➝ x = 360°/24

➝ x = 15°

Verification:-

➝ 6x + 5x + 8x + 5x = 360°

• Put x = 15°

➝ (6×15)° + (5×15)° + (8×15)° + (5×15)° = 360°

➝ 90° + 75° + 120° + 75° = 360°

➝ 360° = 360°

Hence, Verified.

6x = 6×15 = 90°

5x = 5×15 = 75°

8x = 8×15 = 120°

5x = 5×15 = 75°

Therefore,

Angles of quadrilateral are 90°, 75°, 120° and 75°.

Answer 2

$\huge\bold{\mathtt{Question⇒}}$

If the interior angles of the quadrilateral are in the ratio $\mathtt{6:5:8:5},$ what are the measures of its angles?

(a) $\mathtt{90°,\:74°,\:120°,\:76°}$

(b) $\mathtt{100°,\:75°,\:120°,\:75°}$

(c) $\mathtt{90°,\:75°,\:120°,\:75°}$

(d) $\mathtt{100°,\:75°,\:120°,\:75°}$

$\huge\bold{\mathtt{Given⇒}}$

The interior angles of the quadrilateral are in the ratio $\mathtt{6:5:8:5}.$

$\huge\bold{\mathtt{To\:find⇒}}$

The measure of the angles.

$\huge\bold{\mathtt{Solution⇒}}$

Let the angles are $\mathtt{6x°,\:5x°,\:8x°}$ and $\mathtt{5x°}.$

We know that:

${\large\mathtt{The\:sum\:of\:all\: interior\:angles}}\\{\large\mathtt{of\:a\:quadrilateral\:is\:360°.}}$

So, we can say-

$\large\mathtt{6x°+5x°+8x°+5x° = 360°}$

$\large\mathtt{⇒\:24x° = 360°}$

$\large\mathtt{⇒\:x° = ({\frac{360}{24}})°}$

$\large\mathtt{⇒\:x° = 15°}$

$\huge\bold{\mathtt{Hence⇒}}$

$\large\mathtt{x = 15}$

Substituting $\mathtt{x}$ with $\mathtt{24}.$

$\large\mathtt{6x° = (6×15)° = 90°}$

$\large\mathtt{5x° = (5×15)° = 75°}$

$\large\mathtt{8x° = (8×15)° = 120°}$

$\large\mathtt{5x° = (5×15)° = 75°}$

$\huge\bold{\mathtt{Not\:sure\:??}}$

$\huge\bold{\mathtt{Verification⇒}}$

$\large\mathtt{6x°+5x°+8x°+5x° = 360°}$

Putting the measure of the angles.

$\large\mathtt{⇒\:90°+75°+120°+75°= 360°}$

$\large\mathtt{⇒\:360° = 360°}$

So, L.H.S = R.H.S.

Hence, verified.

$\huge\bold{\mathtt{Correct\:Option⇒}}$

(c) $\mathtt{90°,\:75°,\:120°,\:75°}$

$\huge\bold{\mathtt{Done࿐}}$

• $\large\bold{\mathtt{Hope\:this\:helps\:you.}}$

• $\large\bold{\mathtt{Enjoy\: learning\:!!}}$

• $\large\bold{\mathtt{Have\:a\:nice\:day.}}$