Lines a and b are parallel. Line c is a transversal. Find the measures of all angles formed by a, b, and c, One of the angles is 70° bigger than the other
Answers
Answer:
Angles are either 55° or 125°.
Step-by-step explanation:
See the attached diagram.
Let aa' and bb' are two parallel straight lines and cc' is a transversal that meets aa' at o and bb' at o' points.
Now, ∠coa' + ∠coa =180° ..... (1)
Assume by the condition given ∠coa' = x and ∠coa = x+70
Hence, from equation (1), 2x + 70 = 180
⇒ x = 55°
Then ∠coa' =55° and ∠coa = 70+55 = 125°
So, ∠o'oa' = 125° as ∠coa = ∠ o'oa' {Opposite angles}
Again, ∠aoo' = 55° as ∠coa' = ∠aoo' {Opposite angles}
Now, ∠coa' = ∠oo'b' {Corresponding angles} = 55°
and ∠bo'c' = ∠oo'b' = 55° {Opposite angles}
Again ∠oo'b = ∠coa = 125° {Corresponding angles}
and ∠b'o'c' = ∠oo'b =125° {Opposite angles}
(Answer)
Answer:
The 4 angles formed in each case are: ,
,
and
.
Step-by-step explanation:
Line c being transversal implies that it forms 4 angles with lines a and b individually of which 2 in each case are opposite angles, thus are equal.
Let one of the angles be represented by , but the other is greater by
, so that = (
+
)
Thus, we have;
+
+ (
+
) + (
+
) =
( the sum of angles at a point)
+
+
+
+
+
=
+
=
=
-
=
Divide both sides by 4,
=
The other angle is calculated thus,
( +
) =
+
=
Thus the 4 angles formed in both cases have the values; ,
,
and
.
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Answers
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Step-by-step explanation:
Hi, to answer this question, first, we have to calculate the number of years since 1990(x).
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Feel free to ask for more if needed or if you did not understand something.
Answers
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(–3, –2), (0, –5), and (3, 2)
B.
(–3, –2), (0, –5), and (3, –2)
C.
(–3, –8), (0, –5), and (3, 2)
D.
(–3, –8), (0, –5), and (3, –2)
Answers
-2 = -3 - 5, -2 = -8 is wrong which means A is not the answer
B
-2 = -3 -5, -2 = -8 is wrong which means B is not the answer
C
-8 = -3 - 5, -8 = -8
-5 = 0 - 5, -5 = -5
2 = 3 - 5, 2 = -2 is wrong so C is not the answer
D
-8 = -3 -5, -8 = -8
-5 = 0 - 5, -5 = -5
-2 = 3 - 5, -2 = -2
All are correct so D is the answer