A, B, C and D lie on c circle centre O. AC is a diameter of the circle.
AD, BE and CF are parallel lines. Angle ABE = 48 and
angle ACF = 126 .
Find
( a ) angle DAE
First, let's identify some additional angles using the information given:
Angle ACF = 126 degrees (Given)
Angle ACE = 90 degrees (Angle inscribed in a semicircle)
Angle ECF = 126 degrees (Corresponding angles with parallel lines)
Now, we can find angle DAE:
Angle DAE = Angle DAC + Angle CAE
Since AC is a diameter, angle DAC is a right angle, so angle DAC = 90 degrees.
Therefore, Angle DAE = 90 degrees + Angle CAE
Now, we need to find angle CAE:
Angle BAE = Angle BAC + Angle CAE
Angle BAC = 90 degrees (Angle inscribed in a semicircle)
Angle BAE = 48 degrees (Given)
Therefore, 48 degrees = 90 degrees + Angle CAE
Angle CAE = 48 - 90
Angle CAE = -42
Now plug this back into the equation for angle DAE:
Angle DAE = 90 degrees + (-42 degrees)
Angle DAE = 90 - 42
Angle DAE = 48 degrees
Therefore, angle DAE is 48 degrees.