Saved Bookmarks
| 1. |
In the given figure, AB || CD and EF || GH. Find the values of x, y, z and t. |
|
Answer» From the figure we know that ∠PRQ = xo = 60o as the vertically opposite angles are equal We know that EF || GH and RQ is a transversal From the figure we also know that ∠PRQ and ∠RQS are alternate angles So we get ∠PRQ = ∠RQS ∠x = ∠y = 60o We know that AB || CD and PR is a transversal From the figure we know that ∠PRD and ∠APR are alternate angles So we get ∠PRD = ∠APR It can be written as ∠PRQ + ∠QRD = ∠APR By substituting the values we get x + ∠QRD = 110o 60o + ∠QRD = 110o On further calculation ∠QRD = 110o – 60o By subtraction ∠QRD = 50o According to the △ QRS We can write ∠QRD + ∠QSR + ∠RQS = 180o By substituting the values ∠QRD + to + yo = 180o 50o + to + 60o = 180o On further calculation to = 180o – 50o – 60o By subtraction to = 180o – 110o to = 70o We know that AB || CD and GH is a transversal From the figure we know that zo and to are alternate angles So we get zo = to = 70o Therefore, the values of x, y, z and t are 60o, 60o, 70o and 70o. |
|