Question

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Answer 1

Answer:

40°, 60°, 100°, 160°

Correct Question:

The angles of a quadrilateral are in the ratio 2:3:5:8. Find the smallest and greatest angle.

Step-by-step explanation:

Concept used:

→ Sum of all angles in a Quadrilateral is 360°

Solution:

Let the sides of the Quadrilateral be 2x, 3x, 5x and 8x.

Applying the above concept;

2x + 3x + 5x + 8x = 360°

⇒ 18x = 360°

⇒ x = 360° ÷ 18

⇒ x = 20°

For finding the angles of Quadrilateral:

• 2x = 2(20) = 40°
• 3x = 3(20) = 60°
• 5x = 5(20) = 100°
• 8x = 8(20) = 160°

∴ The angles of the quadrilateral are 40°, 60°, 100°, 160°

Answer 2

$\sf \pmb { \underline{SOLUTION - }}$

We are given that,

• The angles of the quadrilateral are in the ratio of 2 : 3 : 5 : 8

We have to find the,

• Smallest and greatest angle = ?

Let us assume that,

• ⟶ First angle be 2x
• ⟶ Second angle be 3x
• ⟶ Third angle be 5x
• ⟶ Fourth angle be 8x

Now,

We know that,

$\underline{ \red{ \boxed{ \sf \: Sum \: of \: all \: the \: angles \: of \: quadrilateral = 360 ^\circ}}}$

Then,

$\rm : \longrightarrow \: \: \: 2x + 3x + 5x + 8x = 360^\circ$

$\rm : \longrightarrow \: \: \: 18x = 360^\circ$

$\rm : \longrightarrow \: \: \: x = \frac{360^\circ}{18}$

$\rm : \longrightarrow \: \: \: x = 20 ^\circ$

Now,

The angles of the quadrilateral are :

• First angle (2x) = 2 × 20° = 40°
• Second angle (3x) = 3 × 20° = 60°
• Third angle (5x) = 5 × 20° = 100°
• Fourth angle (8x) = 8 × 20° = 160°

Therefore,

• The smallest angle is 40°
• The greatest angle is 160°