Question

In the stairs shown below, line s is parallel to line t. The measure of angle 1 is 54 degrees. Find the measure of the remaining angles

Answer 1

∠1 = 54

∠2 = 126

∠3 = 126

∠4 = 54

∠5 = 54

∠6 = 126

∠7 = 126

∠8 = 54

Explanation:

Since s is a straight line,

∠1 + ∠3 = 180

⇒ ∠3 = 180 - ∠1

⇒ ∠3 = 180 - 54

⇒ ∠3 = 126

Vertacally opposite angles:

∠4 = ∠1 and

∠2 = ∠3

⇒ ∠4 = 54

⇒ ∠2 = 126

Corresponding angles:

⇒ ∠3 = 126

∠5 = ∠1

∠6 = ∠2

∠7 = ∠3

∠8 = ∠4

⇒ ∠5 = 54

⇒ ∠6 = 126

⇒ ∠7 = 126

⇒ ∠8 = 54