Question

In the figure (not drawn to scale) given below, if $AD = CD = BC$ and $\angle DBC = 96^\circ$, how much is the value of $\angle DBC$?

• A. 32$^\circ$
• B. 84$^\circ$
• C. 64$^\circ$
• D. Cannot be determined

Hint:

For isosceles triangles, use the angle sum property and symmetry to calculate the base angles.

Answer 1

The Correct Option is C

Given that $AD = CD = BC$ and $\angle DBC = 96^\circ$, the triangle is isosceles, and the base angles are equal. We can calculate the value of $\angle DBC$ using the properties of isosceles triangles and angle sum of a triangle. The base angles of $\triangle BCD$ are: \[ \angle DBC = \frac{180^\circ - 96^\circ}{2} = 64^\circ \] Thus, the value of $\angle DBC$ is 64$^\circ$.