Question

Find the measure of each missing angle.

Answer 1

Explanation:

Angle sum property of triangle: Sum of all the angles of a triangle is 180

Alternate interior angles: When two parallel lines are intersected by a transversal, the pair of angles on the inner side of each of these lines but on the opposite side of the transversal are called alternate interior angles

In ΔABC,

∠1 + 90 + 38 = 180 {angle sum property of triangle}

∠1 + 128 = 180

∠1 = 180 - 128

`\sf \boxed{\bf \angle 1 = 52^ \°}`

AB // CD and AC is transversal.

`\sf \boxed{\bf \angle 3 = 38^\circ}` {Alternate interior angles are equal}

In ΔACD,

∠2 + ∠3 + 63 = 180 {angle sum property of triangle}

∠2 + 38 +63 = 180

∠2 + 101 =180

∠2 = 180 - 101

`\sf \boxed{\bf \angle 2 = 79^ \°}`