Question

The sum of the four angles of a quadrilateral is 360^ .

(i) The angles of quadrilateral are in the ratio

8:1:5:6. Find the measure of each angle. (a) 190 degrees, 260 degrees 130 degrees and 140 degrees

(b) 70 degrees 18 degrees, 144 degrees and 90 degrees

(c) 144°, 18 degrees, 90 degrees and 108 degrees

(d) 108 degrees , 78 degrees 18 degrees and 90°

Answer 1

$\sf\large\underline{Question :-}$

• The sum of the four angles of a quadrilateral is 360^ .The angles of quadrilateral are in the ratio 8:1:5:6.

$\sf\large\underline{Answer:-}$

• Angle I = 144°
• Angle II = 18°
• Angle III = 90°
• Angle IV = 108°

$\sf\large\underline{Solution:-}$

• Let the angles of the quadrilateral be 'x'
• The ratio given is 8:1:5:6
• Let angle I = 8x
• Angle II = 1x
• Angle III = 5x
• Angle IV = 6x

$\red\mapsto$ Sum of all angles of a quadrilateral = 360°

$\red\mapsto$Angle I + Angle II +Angle III + Angle IV = 360°

$\red\mapsto$8x + 1x + 5x + 6x = 360°

$\red\mapsto$20x = 360°

$\red\mapsto\bold{x \: = \cancel\dfrac{360}{20}}$

$\red\mapsto$ x = 18

• $\purple\bigstar$Angle I = 8x => 8 × 18 => 144°
• $\purple\bigstar$Angle II = 1x => 1 × 18 => 18°
• $\purple\bigstar$Angle III = 5x => 5 × 18 => 90°
• $\purple\bigstar$Angle IV = 6x => 6 × 18 => 108°

Answer 2

c) Option c is ✔

144°, 18°, 90° and 108°

$\:$

❖ Step-by-step explanation :

❒ Given :-

➠ The sum of the four angles of a quadrilateral is 360°

➠ The angles of quadrilateral are in the ratio 8:1:5:6.

$\:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\:$

❒ To Find :-

➠ The measure of each angle in a quadrilateral

$\:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\:$

❒ Used Formula :-

$\bf \purple⟼\red{ \: Sum \: of \: all \: angles \: _{(Quadrilateral)}= 360°}$

$\:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\:$

❒ Solution :-

In Quadrilateral,

Sum of all angles = 360°

The angles are in ratio 8:1:5:6

Let,

• First angle = 8x

• Second angle = x

• Third angle = 5x

• Fourth angle = 6x

So,

$\bf ⟹ \: Sum \: of \: all \: angles \: _{(Quadilateral)}= 360°$

$\bf ⟹ \: 8x + x + 5x + 6x= 360°$

$\bf ⟹ \: 20x= 360°$

$\displaystyle\bf ⟹ \: x= \cancel\frac{360}{20}$

$\red{⟹ \: \underline{ \boxed{ \bf x = 18}}}$

Now,

➠ First angle = 8x = 18×8 = 144°

➠ Second angle = x = 18°

➠ Third angle = 5x = 18×5 = 90°

➠ Fourth angle = 6x = 18×6 = 108°

Hence,

All angles in a quadrilateral is 144°, 18°, 90° and 108°

$\:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\:$

❒ Verification :-

$\bf ⟹ \: Sum \: of \: all \: angles \: _{(Quadrilateral)}= 360°$

$\bf ⟹ \: 144° + 18° + 90° + 108°= 360° \:$

$⟹ \: \boxed{ \bf360°= 360° }$

Hence, verified !

$\:$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\:$