Question

3. The measures of the angles of a quadrilateral are in the ratio 1 : 2:3:4. Find the measure of each angle. What type
(HOTS) (
Solution :​

Answer 1

${\underline{\green{\bold{Answer:}}}}$

• 36°
• 64°
• 108°
• 144°

$\underline \orange{ \sf Given : }$

Ratios of sides of quadrilateral are 1:2:3:4

$\underline{\sf \purple{ To \: \: find : }}$

Angles of quadrilateral

$\underline{ \sf \pink {Assumption :}}$

Let ratios be x:2x:3x:4x

$\underline{\sf \red{Solution :}}$

X+2x+3x+4x=360°

10x=360°

x=36°

Angles are:-

$\sf{:⟹ x=36°}\\ \sf{:⟹ 2x=64°}\\ \sf{:⟹ 3x=108}\\ \sf{:⟹ 4x=144°}$

$\underline { \pink{ \sf \: Property \: used :} }$

Angle sum property of quadrilateral.

It means sum of all angles of quadrilateral is 360°.

Answer 2

Answer:

${\underline{\green{\bold{Answer:}}}}$

36°

64°

108°

144°

$\underline \orange{ \sf Given : }$

Ratios of sides of quadrilateral are 1:2:3:4

$\underline{\sf \purple{ To \: \: find : }} </p><p>$

Angles of quadrilateral

$\underline{ \sf \pink {Assumption :}} </p><p>$

Let ratios be x:2x:3x:4x

$\underline{\sf \red{Solution :}} </p><p>$

X+2x+3x+4x=360°

10x=360°

x=36°

Angles are:-

$\begin{gathered}\sf{:⟹ x=36°}\\ \sf{:⟹ 2x=64°}\\ \sf{:⟹ 3x=108}\\ \sf{:⟹ 4x=144°}\\\end{gathered}$

$\underline { \pink{ \sf \: Property \: used :} } </p><p>$

Angle sum property of quadrilateral.

It means sum of all angles of quadrilateral is 360°.