How do I solve this linear equation? Angles A and B are in a quadrilateral are in ratio 2:3, angle C is 30 degrees more than angle B and angle D is 90 degrees.
Firstly I would draw a diagram of a quadrilateral and label my angles, starting clockwise A,B C and D.
Remember that all angles in a quadrilateral add up to 360 degrees.
You must use linear equations to sole this problem. So we can let the unknown angles be represented by some multiple of 'X' i.e. angle=X
As the angles A and B are in a ratio 2:3, this basically means that A=2X and B is of the value 3X.
As C is 30 degrees more than B, C can be represented as 3X+30, as it is basically C=B+30.
Finally D=90
Method:
1)As you know all of the angles in a quadrilateral add up to 360 degrees, we can add up all of these angles so that they should in total add up to 360 degrees.
2)This can be put in a linear expression:
A+B+C+D=360
substituting the values for multiples of X
2X+3X+(3X+30)+90=360
3)total up the 'x' values 8X+30+90=360
4)Put all the unknowns to the left hand side of the equation and the known values to the right hand side
8X=360-30-90 The expression simplifies to 8X=240
5)Now sole for X and substitute the value for x into the expression for A and B and C to find their values
(Answer: X=15 so A=30, B=45, C=75 and D=90)
