Question

From the given figure, find out the values of a and b. when
A = (a + 9) ; B = (2a + 3)º
C = (5b + 6)° and D = (45 – 3)º​

Answer 1

Step-by-step explanation:

A+C=180

a+9+5b+6=180

a+5b+15=180

a+5b=165...............(1)

B+D=180

2a+3+4b-3=180

2a+4b=180

a+2b=90........(2)multiply by 2

subtracting equation 1and 2

a+5b=165

-

a+2b=90

________

3b=75

b=25

put b=25 in equation 1

a+5(25)=165

a =40

(a)=40 &(b)=25

Answer 2

Step-by-step explanation:

we know sum of opposite angles of cyclic quadrilateral is 180 deg.

It means,

$a + c = 180 \: and \: \: b + c = 10 \\ (a + 9) + (5b + 6) = 180 \: \: and \: (2a + 3) + (4b - 3) = 180 \\ a + 5b + 15 = 180 \: \: \: and \: 2a + 4b = 180 \\ a + 5b = 165 \: and \: 2a = 180 - 4b \\ a + 5b = 165 \: and \: a = \frac{180 - 4b}{2} \\ a + 5b = 165 \: and \: a = 90 - 2b \\ 90 - 2b + 5b = 165 \\ 90 + 3b = 165 \\ 3b = 75 \\ b = 25 \\ a = 40$