Question

Q-4) The ratio of four angles in order of a quadrilateral is 2:4:5:4then the measure of the smallest angle of the
quadrilateral is ............. *
O A) 120°
O B) 96°
O C) 48°
O D) 60°​

Answer 1

Answer:

C. 48°

Step-by-step explanation:

Let the common multiple of ratio will be x.

Sum of interior angle of a quadrilateral = 360°

2x + 4x + 5x + 4x = 360°

15x = 360°

x = 360/15

x = 24°

The smallest angle here is 2x.

2x = 2(24) = 48°

Answer 2

✯ ᴀɴsᴡᴇʀ ✯

given →

☞ Ratio of four angle of a quadrilateral is 2:4:5:4

to find →

☞ value of smallest angle of quadrilateral?

__________________________

solution →

➪ Let four angles of a quadrilateral are 2x , 4x , 5x and 4x

★ we know that sum of all interior angles of a quadrilateral is 360°

$: \implies \: 2x + 4x + 5x + 4x = 360 \\ \\ : \implies \: 15x = 360 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \: x = \frac{360}{15} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies \: x = 24\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

so, x = 24 is a common multiple of angles of this quadrilateral.

➜ angles of quadrilateral are;

☆ 2x = 2 × 24 = 48°

☆ 4x = 4 × 24 = 96°

☆ 5x = 5 × 24 = 120°

☆ 4x = 4 × 24 = 96°

here, 120° > 96°= 96° > 48°

hence, measure of smallest angle of the quadrilateral is 48°

➪ option C is correct ✔︎