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Question
In the given figure, AB and CD are parallel lines and XY is a transversal to them. If ∠APX = 110°, ∠XPB = (m+10)°, ∠PQC = (n-20)°, ∠PQD = 70°, find the value of m+n.
In the given figure, AB and CD are parallel lines and XY is a transversal to them. If ∠APX = 110°, ∠XPB = (m+10)°, ∠PQC = (n-20)°, ∠PQD = 70°, find the value of m+n.
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Solution
The correct option is B 190
Given,
AB || CD, ∠APX = 110°,
∠XPB = (m+10)°, ∠PQC = (n-20)°,
∠PQD = 70°
When a line intersects any two given lines, the angles formed at the same relative position at each intersection are called corresponding angles.
If two given lines are parallel and there is a transversal, then corresponding angles are equal in measure.
∴ ∠XPB = ∠PQD
⇒ (m+10)° = 70°
⇒ m + 10 = 70
⇒ m = 60
∴ ∠XPA = ∠PQC
⇒(n-20)° = 110°
⇒ n - 20 = 110
⇒ n = 130
∴ m + n = 60 + 130
= 190
Given,
AB || CD, ∠APX = 110°,
∠XPB = (m+10)°, ∠PQC = (n-20)°,
∠PQD = 70°
When a line intersects any two given lines, the angles formed at the same relative position at each intersection are called corresponding angles.
If two given lines are parallel and there is a transversal, then corresponding angles are equal in measure.
∴ ∠XPB = ∠PQD
⇒ (m+10)° = 70°
⇒ m + 10 = 70
⇒ m = 60
∴ ∠XPA = ∠PQC
⇒(n-20)° = 110°
⇒ n - 20 = 110
⇒ n = 130
∴ m + n = 60 + 130
= 190
Suggest Corrections
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and 
are parallel lines. The transversals 
and 
intersect at U on the line