Three angles of a quadrilateral are in the ratio 3:4:5. The difference of the least and the greatest of these angles is 45. Find the fourth angles of the quadrilateral.
Answers
Given:
✰ Three angles of a quadrilateral are in the ratio 3:4:5.
✰ The difference of the least and the greatest of these angles is 45.
To find:
✠ The fourth angle of the quadrilateral.
Solution:
First, we will assume that the measure of three angles of a quadrilateral are 3x, 4x and 5x respectively. Then, we know that the difference of the least and the greatest of these angles is 45. So, we will substract the least angle from the greatest angle of the quadrilateral, which is equal to 45. So, we will form requisite equation and find out the value of x. After that we will substitute the value of x in these given angles to find the three angels of the quadrilateral.
Let's see how...
Let the measure of three angles of a quadrilateral are 3x, 4x and 5x respectively.
The difference of the least and the greatest of these angles is 45.
➛ 5x - 3x = 45
➛ 2x = 45
➛ x = 45/2
➛ x = 22.5°
Find out the respective angles,
⟹ First angle = 3x
⟹ First angle = 3 × 22.5
⟹ First angle = 67.5°
⟹ Second angle = 4x
⟹ Second angle = 4 × 22.5
⟹ Second angle = 90°
⟹ Third angle = 5x
⟹ Third angle = 5 × 22.5
⟹ Third angle = 112.5°
Now, we will use angle sum property of quadrilateral to find out the forth angle.
According to the angle sum property of quadrilateral.
The sum of all the angles of a quadrilateral is 360°
Let the forth angle of a quadrilateral be y
➤ 67.5 + 90 + 112.5 + y = 360
➤ 157.5 + 112.5 + y = 360
➤ 270 + y = 360
➤ y = 360 - 270
➤ y = 90°
∴ The fourth angle of the quadrilateral = 90°
_______________________________
Given,
- Three angles of a quadrilateral are in the ratio 3:4:5.
- The difference of the least and the greatest of these angles is 45.
To Find,
- The Fourth angle of the Quadrilateral.
Solution,
Let's,
The First angle = 3X
So,
The Second angle = 4X
So,
The Third angle = 5X
As Given,
5X - 3X = 45°
→ 2X = 45°
→ X = 45°/2
→ X = 22.5°
Therefore,
The First angle = 3X
→ The First angle = 3(22.5°)
→ The First angle = 67.5°
The Second angle = 4X
→ The Second angle = 4(22.5°)
→ The Second angle = 90°
The Third angle = 5X
→ The Third angle = 5(22.5°)
→ The Third angle = 112.5°
Let's,
The Fourth angle = Y
The Sum of All angles of A Quadrilateral = 360°
→ 3X + 4X + 5X + Y = 360°
→ 67.5° + 90° + 112.5° + Y= 360°
→ 270° + Y = 360°
→ Y = 360° - 270°
→ Y = 90°
Required Answer,
The Fourth angle of Quadrilateral = 90°