Attempt following question by selecting a choice to answer.
c
AB and CD are two parallel lines and
∠x = 90o. Find the measures of
∠1, ∠4, and
∠6.cc ccA.
c100
oB.
c80
oC.
c90
oD.
cNone of the above
c
C
Step 1: ∠x and ∠2 are vertical angles.[From the figure.]
Step 2: ∠x = ∠2 = 90o[Vertical angles are congruent.]
Step 3: ∠1 and ∠2 are supplementary angles.[From the figure.]
Step 4: ∠1 + ∠2 = 180o
[Sum of supplementary angles is 180o.]
Step 5: ∠1 = 180o - ∠2 = 90o[Substitute ∠2 = 90o.]
Step 6: ∠2 and ∠4 are alternate interior angles.[From the figure.]
Step 7: ∠4 = ∠2 = 90o[Alternate interior angles are congruent.]
Step 8: ∠4 and ∠6 are vertical angles.[From the figure.]
Step 9: ∠6 = ∠4 = 90o[Vertical angles are congruent.]
Step 10: So, ∠1 = ∠4 = ∠6 = 90o