Question

Find the measure of each of the numbered angles. Explain your reasoning for each angle

Answer 1

∠1 = 47

∠2 = 63

∠3 = 70

∠4 = 70

Explanation:

∠2 and 63 are alternate interior angles. Alternate interior angles are equal.

∠2 = 63

∠3 and 110 are linear pair angles. Sum of linear pair angles is 180.

∠3 + 110 = 180

∠3 = 180 - 110

∠3 = 70

GDEF is a parallelogram, so ∠DGF = ∠DEF

That is,

∠3 = ∠4

∠4 = 70

∠1, ∠2 and ∠3 are interior angles in a triangle.

Sum of interior angles in a triangle is 180,

∠1 + ∠2 + ∠3 = 180

∠1 + 63 + 70 = 180

∠1 + 133 = 180

∠1 = 180 - 133

∠1 = 47