Question

In Figure 4, ABCD is a rectangle. Its diagonals AC and BD intersect each
other at O. AC is produced to E such that ECD is 140°. Find the measure of the
angles of triangle AOB.
​​

Answer 1

Answer:

Angle AOB = 90°

Step-by-step explanation:

1) Angle DCO is 40° (Angle of st.line {180-140})

2) Angle DCO = Angle ADO (Angles are corresponding)

3). Angle ODC = 50° ( Angles of an rectangle {90-40})

4) Angle DOC = 90° ( Sum of Angles In triangle { 180-[50+40]})

5) Angle AOB = DOC (Opposite angles)

Answer 2

∠ECD = 140°

∠OCD + ∠ECD = 180°

∠OCD = 180° - 140°

∠OCD = 40°

∠OCD = ∠OAB = 40°

In rectangle, all angles equal 90° and angles of diagonals to the sides are equal

∴∠OAB = ∠OBA = 40°

We know that the sum of angles of a triangle equals 90°

∴∠AOB = 180° - 40° - 40°

. = 100°

Thus, the angles of ΔAOB are 40°, 40° and 100°.