In Quadrilateral ABCD, the measures of <A, <B, <C and <D are in the ration 1 : 2 : 3 : 3, respectively. Find the
measure of the four angles.
Answers
Answer:
The quadrilateral has angles measuring 40°, 80°, 120° and 120°.
Step-by-step explanation:
Given that the ratios of the angles of a quadrilateral is 1 : 2 : 3 : 3
Let the multiplying factor be 'x'
Therefore, the angles will be x, 2x, 3x and 3x
We know that sum of all the interior angles of a quadrilateral is 360°
Therefore x + 2x + 3x + 3x = 360°
=> 9x = 360°
=> x = 360/9
=> x = 40°
Therefore, the angles will be x= 40°
2x = 80°
3x = 120°
Therefore, the quadrilateral has angles measuring 40°, 80°, 120° and 120°.
Step-by-step explanation:
Solution :
∠A : ∠B : ∠C : ∠D = 1 : 2 : 3 : 3
Let,
- I st angle (∠A)= x
- II nd angle (∠B) = 2x
- III rd angle (∠C) = 3x
- IV th angle (∠D) = 3x
★ According to the Question :
∠A + ∠B + ∠C + ∠D = 360°
⇒ x + 2x + 3x + 3x = 360
⇒ 9x = 360
⇒ x = 360/9
⇒ x = 40
I st angle (∠A)= 40°
• II nd angle (∠B) = 2x
⇒ 2(40) = 80
II nd angle (∠B) = 80°
• III rd angle (∠C) = 3x
⇒ 3(40) = 120
III rd angle (∠C) =120°
• IV th angle (∠D) = 3x
⇒ 3(40) = 120
IV th angle (∠D) = 120°
- 40° + 80° + 120° + 120° = 360°
Therefore, angles are 40°, 80°, 120° and 120°.