In a cyclic quadrilateral

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

In a cyclic quadrilateral WXYZWXYZ, the measures of the four interior angles are represented by ∠W=(2x+15)∘,  ∠X=(3y−5)∘,  ∠Y=(5x−25)∘\angle W=(2x+15)^\circ,\; \angle X=(3y-5)^\circ,\; \angle Y=(5x-25)^\circ and ∠Z=(4y+5)∘\angle Z=(4y+5)^\circ. (i) Write the two equations that arise from the property of opposite angles in a cyclic quadrilateral. (ii) Solve the simultaneous equations to obtain the values of xx and yy. (iii) Hence calculate the measures of ∠W,  ∠X,  ∠Y\angle W,\; \angle X,\; \angle Y and ∠Z\angle Z. (iv) Verify that each pair of opposite angles adds up to 180∘180^\circ.

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