Question

in the given figure, AD||BC. Find the measures of unknown angles. ∠BAE= ° ∠EAD= ° ∠ADC= °

Answer 1

Step-by-step explanation:

AD ║BC and AB is the transversal
∴∠DAB + ∠ABC = 180°  -( Adjacent angles are supplementary)
∴∠DAB + 60° = 180°
∴∠DAB = 180 - 60
∵∠DAB = 120°               -(i)

AD ║BC and AE is the transversal.
∴∠DAE +∠ AEC = 180°   -( Adjacent angles are supplementary)
∴∠DAE + 80° = 180°
∴∠DAE = 180-80
∴∠DAE = 100 °    -(ii)

∴∠BAE = ∠DAE - ∠DAB
            =100-120                     -[From (i) and (ii)]
            =20°  -(iii)            -

AD║BC an DC is the transversal.
∴∠ADC + ∠DCE = 180° -( Adjacent angles are supplementary)
∴∠ADC + 50° =180°
∴∠ADC = 180-50
∴∠ADC = 130°    -(iv)

∴∠BAE= 20° ,∠EAD =100 ° and ∠ADC= 130° -[ From (ii),(iii) and (iv) ]