Question

are 11. AD and CE are respectively perpendiculars
to sides BC and AB of AABC.
If ZECD = 45°, find ZBAD.
Determine the angles of each of the following triangles.​

Answer 1

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In ∆DOC:-⠀⠀⠀

angle ECD = 45°⠀⠀...(Given)

angle ODC = 90°⠀...(AD is perpendicular to BC)

angle ECD + angle ODC + angle COD = 180° ...(Angle Sum Property of ∆)

45° + 90° + angle COD = 180°⠀⠀⠀

135° + angle COD = 180°⠀ ⠀⠀

angle COD = 180° - 135°⠀⠀⠀

angle COD = 45°⠀⠀⠀⠀

angle COD = angle AOE ...(Vertically opposite angles)

angle AOE = 45°⠀⠀⠀⠀⠀

In ∆ AOE:-⠀

angle AEC= 90°...(CE is perpendicular to AB)

angle AOE = 45°⠀...(proved above)

angle AEC + angle AOE + angle BAD = 180°⠀⠀...(Angle Sum Property of ∆)

90°+ 45° + angle BAD = 180°⠀

135° + angle BAD = 180°⠀

angle BAD = 180° - 135°

angle BAD = 45°⠀

Your Answer = angle BAD = 45°