Lines RS and TU intersect at point O

MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

Lines RS and TU intersect at point O. Let ∠ROU=(2x+y)∘\angle ROU = (2x + y)^{\circ}, ∠UOS=(3x+y)∘\angle UOS = (3x + y)^{\circ}, and ∠SOT\angle SOT (which is opposite to ∠UOS\angle UOS) be (4x−y)∘(4x - y)^{\circ}. (i) Using the relationships among the given angles, frame two independent linear equations in xx and yy. (ii) Solve the simultaneous equations to obtain the values of xx and yy. (iii) Hence find the measure of each of the four angles formed at O. (iv) Classify each of the four angles as acute or obtuse, giving reasons for your answer.

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