Question

In the diagram,
c + d = 150 \: degreec+d=150degree
find the value of a+b,if c is half of d.​

Answer 1

Answer:

a+b=50

d/2=c. .......(1)

Step-by-step explanation:

150-c = d

Putting value of "d" in equation (1)

150-c/2=c

150-c=2c

2c+c=150

3c=150

c=150/3

c=50.

Putting value of "c" in equation (1)

d/2=c

d/2=50

d=2(50)

d=100

angle BOD= 180-100. (straight line angle)

BOD= 80

IN TRIANGLE BOD;

angle a+BOD+OBD= 180 .......(2)

SIMILARLY IN TRIANGLE POC

ANGLE b+POC+OPC=180 ........(3)

EQUATION (2)=EQUATION (3)

a+BOD+OBD=b+POC+OPC=180

a+80+OBD=b+80+OPC. (angle BOD=POC=80)

a+OBD=b+OPC

angle c+b= angle CBD (sum of opposite interior angles)

angle BOD =80

angle c=50

in triangle BOD

angle a+BOD+CBD=180

a+80+c+b=180

a+80+50+b=180

a+b=180-130

a+b=50

YOU MAY NOT UNDERSTAND SOLUTION BCOZ I HAVE NOT GIVEN THE REASON BUT ANSWER IS CORRECT.

Answer 2

Step-by-step explanation:

see the attachment.............