CUET UG 2023 — General Test Geometry

1. Finding the value of $y$y:

The angles at vertex $A$A lie on a straight line. Therefore, the interior angle $\angle A$∠A inside the triangle and the exterior angle $100^\circ$100∘ form a linear pair (adding up to $180^\circ$180∘):

\angle A = 180^\circ - 100^\circ = 80^\circ$ Now, looking inside the triangle $\triangle ABC$, the sum of all interior angles must be \$180^\circ$:\angle A + \angle B + y = 180^\circ$\$80^\circ + 50^\circ + y = 180^\circ

\130^\circ + y = 180^\circ$$$$y = 50$

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2. Finding the value of $x$x:

The angles $x^\circ$x∘ and $y^\circ$y∘ lie on a straight horizontal line at vertex $C$C, making them a linear pair:

$$x + y = 180^\circ$$x+y=180∘

$$x + 50^\circ = 180^\circ$$x+50∘=180∘

$$x = 130$x=130

(Alternatively, by the exterior angle theorem, $x$x is equal to the sum of the two opposite interior angles: $x = \angle A + \angle B = 80^\circ + 50^\circ = 130$x=∠A+∠B=80∘+50∘=130.)

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Conclusion:

• $x = 130$x=130
• $y = 50$y=50