Question

In the given figure, AB || CD. If AEF - 75°, ZGHF = 35º and EGH = r, find the value of r IP E F 35 H D​

Answer 1

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Answer 2

Answer:

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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.

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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=35°

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

So we get

∠GHD=∠QHP=35°

We know that the sum of all the angles in triangle DQHP is 35° .

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

∠PQH+∠QHP+∠QPH=180°

By substituting the values we get

∠PQH+35°+90°=180°

On further calculation

∠PQH=180° −35° −90°

By subtraction

∠PQH=180° −125°

∠PQH=55°

Therefore, ∠PQH=55°