Question

In the given figure, find the measures of Angle x and Angle y​

Answer 1

`\large\underline{\sf{Solution-}}`

From the given given figure, we have been asked to calculate the value of x and y.

Clearly, in the given figure we can say that ∠ABC and ∠ABD are forming a linear pair. As, we know that the sum of the angles which form a linear pair is 180°. Henceforth, the sum ∠ABC and ∠ABD will be 180°. Writing this statement in the form of an equation,

`\rm { \angle ABC + \angle ABD = 180^\circ} \\ \\ \longmapsto \rm { x^\circ + 70^\circ= 180^\circ} \\ \\ \longmapsto \rm { x^\circ = 180^\circ - 70^\circ} \\ \\ \longmapsto \boxed{\bf { x^\circ = 110^\circ}}`

Therefore, the value of x is 110°.

Now, we have to calculate the value of y. Here, we'll apply the exterior angle property of triangle to calculate the value of y. The sum of the interior opposite angles of a triangle gives the measurement of the exterior angle of the triangle. Here, the two interior opposite angles of ∆ABC are ∠A and ∠C and the exterior angle is ∠ABD. Writing this statement in the form of an equation,

`\rm { \angle A + \angle C = \angle ABD } \\ \\ \longmapsto \rm { 25^\circ + y^\circ = 75^\circ } \\ \\\longmapsto \rm { y^\circ = 70^\circ - 25^\circ} \\ \\ \longmapsto \boxed{\bf { y^\circ = 45^\circ}}`

Therefore, the value of y° is 45°.