Question

PLSSS HELP!!! 40 pts!!!!

Using what you know about angles and translations, find all of the angle
measures in the image below.

Answer 1

∠1=135°

∠2=45°

∠3=45°

∠4=135°

∠5=135°

∠6=45°

∠7=45°

∠8=135°

Explanation:

→∠1=∠4[Being vertically opposite angles]

→∠4=135°

→∠1=∠5[Corresponding angles]

→∠5=135°

→∠5=∠8[Being vertically opposite angles]

→∠8=135°

→∠1+∠2=180°[Sum of linear pair]

→∠2=180°-135°

→∠2=45°

→∠2=∠3[Being vertically opposite angles]

→∠3=45°

→∠3=∠6[Alternate angles]

→∠6=45°

→∠6=∠7[Being vertically opposite angles]

→∠7=45°

Answer 2

∠1 = 135°

∠2 = 45°

∠3 = 45°

∠4 = 135°

∠5 = 135°

∠6 = 45°

∠7 = 45°

∠8 = 135°

Explanation:

• The diagram shows two lines that are intersected by a transversal. (A transversal is a line that passes through two lines in the same plane at two distinct points).

• When two lines are intersected by a transversal, the angles in matching corners are called Corresponding Angles
  So ∠1 = ∠5 , ∠2 = ∠6 , ∠3 = ∠7 , ∠4 = ∠8

• Angles on one side of a straight line always add to 180°

Using the Angles on a Straight Line theorem

Angle 1 and 2 are on a straight line, so

∠2 = 180 - ∠1 = 180 - 135 = 45°

Similarly,

∠3 = 180 - ∠1 = 180 - 135 = 45°

∠4 = 180 - ∠3 = 180 - 45 = 135°

Using the Corresponding Angles theorem

As ∠1 = ∠5, then ∠5 = 135°

As ∠2 = ∠6, then ∠6 = 45°

As ∠3 = ∠7, then ∠7 = 45°

As ∠4 = ∠8, then ∠8 = 135°