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

Answer:

let an angle be X

ATQ....

6x+5x+8x+5x=360

(sum of all angles in quadrilateral is always 360)

24x = 360

X = 360/24

X= 15.

now the all angles are.

6x = 6*15 = 90

5x = 5*15= 75

8x= 8×15 = 120

5x= 5*15= 75.

Option A is correct.

I hope you understand

Answer 2

$\huge\bold{\mathtt{Question⇒}}$

If the interior 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) ${100°,\:75°,\:120°,\:75°}$

$\huge\bold{\mathtt{Given⇒}}$

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

$\huge\bold{\mathtt{To\:find⇒}}$

The measure of the angles.

$\huge\bold{\mathtt{Solution⇒}}$

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

We know that:

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

So, we can say-

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

$\large{⇒\:24x = 360}$

$\large{⇒\:x = ({\frac{360}{24}})}$

$\large{⇒\:x = 15}$

$\huge\bold{\mathtt{Hence⇒}}$

$\large{x = 15}$

Substitute ${x}$ with ${24}.$

$\large{6x° = (6×15)° = 90°}$

$\large{5x° = (5×15)° = 75°}$

$\large{8x° = (8×15)° = 120°}$

$\large{5x° = (5×15)° = 75°}$

$\huge\bold{\mathtt{Confused\:??}}$

$\huge\bold{\mathtt{Verification⇒}}$

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

Put the measure of the angles.

$\large{⇒\:90+75+120+75= 360}$

$\large{⇒\:360 = 360}$

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

Hence, verified.

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

(c) ${90°,\:75°,\:120°,\:75°}$

$\huge\bold{\mathtt{Done}}$

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

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