Question

Find the measure of each numbered angle

Answer 1

∠ 1 = 69° , ∠ 2 = 37° , ∠3 = 106° , ∠ 4 = 21°

Explanation:

∠ 2 and 53° form a right angle (90°) , that is

∠ 2 + 53° = 90° ( subtract 53° from both sides )

∠ 2 = 37°

the sum of the 3 angles in a triangle = 180°

consider the triangle with ∠ 1 and ∠ 2 , then

∠ 1 + ∠ 2 + 74° = 180° ( substitute ∠ 2 = 37° )

∠ 1 + 37° + 74° = 180°

∠ 1 + 111° = 180° ( subtract 111° from both sides )

∠ 1 = 69°

∠ 3 and 74° are a linear pair and sum to 180° , that is

∠ 3 + 74° = 180° ( subtract 74° from both sides )

∠ 3 = 106°

Then in the triangle with ∠ 3 and ∠ 4 , summing the angles

∠ 3 + ∠ 4 + 53° = 180° ( substitute ∠ 3 = 106° )

106° + ∠ 4 + 53° = 180°

159° + ∠ 4 = 180° ( subtract 159° from both sides )

∠ 4 = 21°

So ∠ 1 = 69° , ∠ 2 = 37° , ∠ 3 = 106° , ∠ 4 = 21°