The measurements of ∠1 = 60°, ∠2 = 30° and ∠3 = 90°.
Solution:
By the property of rectangle,
Opposite sides of rectangle are parallel.
By another property of parallel lines,
If two parallel lines cut by a transversal (diagonal) then alternate interior angles are congruent.
60° and ∠1 are alternate interior angles.
Hence m∠1 = 60°.
In rectangle, all the angles are right angle.
m∠1 + m∠2 = 90°
60° + m∠2 = 90°
Subtract 60° from both sides of the equation.
m∠2 = 30°
In rectangle, all the angles are right angle.
m∠3 = 90°
Hence the measurements of ∠1 = 60°, ∠2 = 30° and ∠3 = 90°.
