the sum of two angles of a quadrilateral is 150 and the other two angles are in ratio 2:3. Find the measure of each angles?
Maths
Sum of angles of a quadrilateral = 360°
sum of the other two (C & D) = 360-150=210
If C : D = 2:3, then
C+D=210,
C: C+D = 2 : 5 = 84 : 210
C=84, D=210-84=126
The first two angles (A & B) add up to 150, which could be A=100, B=50, or A=75, B=75, etc. Without additional information, there is an infinite set of solutions for A and B.
how to find a,b
To find the measures of the angles, we'll follow these steps:
Step 1: Identify what we know
We are given that the sum of two angles in the quadrilateral is 150 degrees. Let's label these angles as A and B. We are also told that the other two angles are in a ratio of 2:3. Let's label these angles as C and D.
Step 2: Set up equations using the given information
Since the sum of two angles is 150 degrees, we can write the equation:
A + B = 150
For the angles C and D, since they are in a ratio of 2:3, we can write the equation:
C/D = 2/3
Step 3: Solve the equations
From equation 2, we can rearrange it to:
C = (2/3)D
Substituting this value of C into equation 1, we have:
A + B = 150
(2/3)D + D = 150
(5/3)D = 150
Multiplying both sides by 3/5 to isolate D, we get:
D = (3/5) * 150
D = 90
Now that we know the value of D, we can substitute it back into equation 2 to find C:
C = (2/3) * 90
C = 60
Step 4: Calculate the remaining angles
Now that we have found the values of C and D, we can find the remaining angles A and B by subtracting C and D from 180 degrees, since a quadrilateral has a total angle sum of 360 degrees.
A = 180 - C - D
A = 180 - 60 - 90
A = 30
B = 180 - C - D
B = 180 - 60 - 90
B = 30
So, the measures of the angles are:
A = 30 degrees
B = 30 degrees
C = 60 degrees
D = 90 degrees