Question

4. The angles of a quadrilateral are in the ratio 2:3:5:8. Find the measure of the largest angle.

Answer 1

Answer:

Complete step-by-step answer:

We will use the fact that the sum of angles of a quadrilateral is 360∘.

Sum of angles of quadrilateral is 360∘ ………(1)

Now, we have the ratio of angles as 2 : 3 : 5 : 8.

Let the first angle be 2x, so then according to the ratio, the angles will be 2x,3x,5x,8x.

Now using (1), we will have:-

2x+3x+5x+8x=360∘

Simplifying the LHS, we will have:-

18x=360∘

Taking the 15 from multiplication in LHS to division in RHS, we will have:-

x=360∘18=40∘2=20∘

Hence, x=20∘.

So, the angles will be 40∘,60∘,100∘,160∘.

∴ The smallest angle of the quadrilateral = 40∘

largest angle is 160

Answer 2

Answer :

• Largest angle = 160°

Given :

• The ratio of angles in a quadrilateral = 2 : 3 : 5 : 8.

To find :

• the measure of the largest angle.

Solution :

⇒ Let's find the angles of the quadrilateral.

• Angles of Quadrilateral = 360°

→ 2x + 3x + 5x + 8x = 360°

→ 5x + 13x = 360°

→ 18x = 360°

$\sf \rightarrow x = \dfrac{360^{\circ}}{18}$

$\sf \rightarrow x = \cancel{\dfrac{360^{\circ}}{18} }$

$\sf \rightarrow x = 20$

$\sf \therefore x = 20$

→ 2x = 2 × 20 = 40°

→ 3x = 3 × 20 = 60°

→ 5x = 5 × 20 = 100°

→ 8x = 8 × 20 = 160°

• Therefore, the angles are 40°, 60°, 100°, and 160°.

⇒ Largest angle = 160°

• Therefore, the largest angle is 160°.