Calculate the angle x and angle y value in the given figure.
The value of the angle x and angle y can be calculated using the congruence property of the triangle.
Answer: The value of angle x is 37º and the value of angle y is 70º.
Let's calculate ∠x and ∠y.
In the figure given below,
In triangle AOB and triangle AOC,
AB = AC (Given)
⇒ ∠ABO = ∠ACO (angles opposite to equal sides are equal)
AO = AO (Common side)
Therefore, triangle AOB is congruent to triangle AOC by SAS property. (If two sides and one angle of any two triangles are congruent then the triangle is congruent.) (Eq. 1)
Similarly, in triangle BOD and triangle COD,
BD = CD (Given)
⇒ ∠DBO = ∠DCO (angles opposite equal sides are equal)
DO = DO (Common side)
Therefore, triangle BOD and triangle COD are congruent by SAS property. (Eq. 2)
Since all parts of congruent triangles are equal.
So ∠x = 37º from (Eq. 1) and ∠y = 70º from (Eq. 2)
Thus, the value of ∠x = 37º and ∠y = 70º