Question

ABC is a triangle. BAD is 40 degrees, DAC is 20 degrees, ABE is 60 degrees and DBE is 10 degrees. What is angle CDE (angle x)?

Answer 1

`x=30^@`

Explanation:

`angleADB=180-angleABD-angleBAD=180-70-40=70^@`
`=> DeltaABD` is isosceles, `=> color(red)(AB=AD)`,
`angleAEB=180-angleABE-angleBAE=180-60-60=60^@`
`=> DeltaABE` is equilateral,
`=> AE=AB, => color(red)(AE=AD)`,
`=> DeltaADE` is isosceles,
`=> angleADE=angleAED=(180-20)/2=80^@`
`=> angleCDE=x=180-angleADB-angleADE=180-70-80=30^@`