The measure of angles ∠1, ∠2 and ∠3 are 62°, 45° and 24° respectively.
From the given figure, measure of angles are 118°, 73° and 49°.
What is exterior angle theorem?
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
From the given figure, 118° + ∠1 = 180°
⇒ ∠1 = 180° - 118°
⇒ ∠1 = 62°
Now, 118° = 73° + ∠2
⇒ ∠2 = 118° - 73°
⇒ ∠2 = 45°
Using angle sum property of a triangle
62° + 49° + (∠2+∠3) = 180°
⇒ 111° + (∠2+∠3) = 180°
⇒ (∠2+∠3) = 180°- 111°
⇒ (∠2+∠3) = 69°
⇒ 45° +∠3 = 69°
⇒ ∠3 = 24°
Therefore, the measure of angles ∠1, ∠2 and ∠3 are 62°, 45° and 24° respectively.