If the figure given below ( not to scale), ABCD, CBEF and EGHF are three congruent squares. Find `angleFAE+angleHAG`.

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

B

Explanation

Let `angleFAE=theta_(1), andangleHAG=theta_(2)`
`tantheta_(1)=(FE)/(AE)=(1)/(2)`
`tantheta_(2)=(HG)/(AG)=(1)/(3)`
`tan(theta_(1)+theta_(2))=(tantheta_(1)+tantheta_(2))/(1-tantheta_(1)tantheta_(2))`
`=((1)/(2)+(1)/(3))/(1-((1)/(2))((1)/(3)))`
`((5)/(6))/((5)/(6))=1`
`tan(theta_(1)+theta_(2))=tan45^(@)`
`rArrtheta_(1)+theta_(2)=45^(@)`
`angleFAE+angleHAG=45^(@)`.