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in Triangles by (44.3k points)

In the given figure, AB || CD and EF is a transversal, cutting them at G and H respectively. If ∠EGB = 35° and QP ⊥ EF, find the measure of ∠PQH.

1 Answer

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We know that AB || CD and EF is a transversal

From the figure we know that ∠EGB and ∠GHD are corresponding angles

So we get

∠EGB = ∠GHD = 35o

From the figure we know that ∠GHD and ∠QHP are vertically opposite angles

So we get

∠GHD = ∠QHP = 35o

We know that the sum of all the angles in triangle DQHP is 180o.

∠PQH + ∠QHP + ∠QPH = 180o

By substituting the values we get

∠PQH + 35o + 90o = 180o

On further calculation

∠PQH = 180o – 35o – 90o

By subtraction

∠PQH = 180o – 125o

∠PQH = 55o

Therefore, ∠PQH = 55o

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