Question

ABCD is a rectangle with diagonals AC and BD intersecting at O. ZAOB = 56. Find ZBAO and ZAOD.​

Answer 1

Answer:

angle BAO = 62°

angle AOD = 124°

Step-by-step explanation:

Consider triangle AOB,

Since, diagonals of rectangle bisect each other

AO=OB

As, angles opposite to equal sides are equal in a triangle

.: angle OAB = angle OBA = x°

.: angle OAB + angle OBA + angle AOB = 180° (angle sum property of triangle)

= x° + x° + 56° = 180°

= 2x° = 180° - 56°

= x° = 124°/2 = 62° (angle BAO)

Since, angle AOB + angle AOD = 180° (Linear pair)

= 56° + angle AOD = 180°

= angle AOD = 180° - 56° = 124°