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Question

# In the adjoining figure line p || line q. Line ‘t′ and line ‘s′ are transversals. Find the measure of ∠x and ∠y using the measures of angles given in the figure.

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Solution

## Given: Line p || line q, line t and line s are transversals. Let us find the measure of ∠x and ∠y. Firstly, Let us consider ∠z as shown in figure. Measure of ∠z=40° … (i) [Since, they are corresponding angles] So, ∠x+∠z=180° [Since, angles are in a linear pair] ∠x+40°=180° [From equation (i)] ∠x=180°−40° ∠x=140° Now, let us consider ∠w as shown in the figure. ∠w+70°=180° [Since, angles are in a linear pair] ∠w=180°−70° ∠w=110° ... (ii) It is given that, line p || line q and line ′s′ is a transversal. So, ∠y=∠w [by using alternate angles] ∠y=110° [From equation (ii)] ∴ The measure of ∠x is 140° and ∠y is 110°.

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