Answers
measure of angle 2 is 56
measure of angle 3 is 74
All triangle’s angles add up to 180
The measure of each numbered angles are ∠1 = 56°, ∠2 = 56° and ∠3 = 74°.
What is Angle?An angle for any figure is formed by two rays which joins at a common point called vertex or node.
Usually angles are measured in degrees or radians.
Consider triangle PMQ
The sum of the interior angles of a triangle is 180°.
∠MPQ + ∠QMP + ∠PQM = 180°
58° + 66° + ∠1 = 180°
∠1 = 180° - (58° + 66°)
∠1 = 180° - 124°
∠1 = 56°
Now, ∠1 and ∠2 are vertically opposite angles. Hence they are equal.
∠2 = 56°.
Again, for triangle NQO
∠2 + ∠3 + 50° = 180°
56° + ∠3 + 50° = 180°
∠3 = 180° - (50° + 56°)
∠3 = 180° - 106°
∠3 = 74°
Hence ∠1, ∠2 and ∠3 are 56°, 56° and 74° respectively.
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