The angles of a quadrilateral are in the ratio 2:3:7. The mean of these angle is 64. Find all the four angles?
Did you mean that 3 of the angles are in the ratio of 2:3:7 ?
let those three angles be 2x, 3x, and 7x
let the fourth angle be y
2x + 3x + 7x + y = 360
y + 12x = 360
y = 360 - 12x
"the mean of these angles is 64"
I will assume you mean the mean of the 3 angles.
12x/3 = 64
4x = 64
x = 16
then y = 360-192 = 168
the 4 angles are : 32° , 48°, 112°, and 168°
2x + 3x + 7x + y = 360
y + 12x = 360
y = 360 - 12x
The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers
2x + 3x + 7x = 12x
2x + 3x + 7x = 3
12x/3 = 64
4x = 64
x = 64/4
= 16
y = 360 - 12x
= 360 - (12x16)
=360 - 192
= 168
<1 = 2x = 2 x 16 = 32
<2 = 3x = 3 x 16 = 48
<3 = 7x = 7 x 16 = 112
<4 = 168 (proved above)
so the 4 <s are 32^, 48^, 112^ and 168^
Answer is 32,48,112,168
To find all four angles of the quadrilateral, we need to determine the value of each angle using the given information.
Step 1: Calculate the sum of the angle ratios.
The sum of the ratios 2:3:7 is 2 + 3 + 7 = 12.
Step 2: Determine the constant factor.
To find the constant factor, we divide the mean of the angles by the sum of the ratios: 64 / 12 = 5.333 (rounded to three decimal places).
Step 3: Calculate the angles.
Multiply the constant factor by each part of the ratio to obtain the angles.
- First angle: 2 * 5.333 ≈ 10.666
- Second angle: 3 * 5.333 ≈ 16
- Third angle: 7 * 5.333 ≈ 37.331
- Fourth angle: Subtract the sum of the three known angles from 360 (the total sum of angles in a quadrilateral).
Fourth angle = 360 - (10.666 + 16 + 37.331) ≈ 295.003
Therefore, the four angles of the quadrilateral are approximately:
10.666°, 16°, 37.331°, and 295.003°.