In triangle $BCD$, which is isosceles with $BC$ congruent to $BD$, what is the measure of angle $CBD$ if angle $C$ is $20°$? Choose the correct answer.

• A. $160°$
• B. $130°$
• C. $120°$
• D. $100°$

Answer: (B)

Verified step by step guidance

1. Identify the given information: triangle BCD is isosceles with sides BC congruent to BD, and angle C measures 20°.
2. Recall that in an isosceles triangle, the angles opposite the equal sides are equal. Since BC = BD, angles opposite these sides, which are angles BDC and BCD, are equal.
3. Label the angles: let angle CBD be \( x \). Since BC = BD, angle BCD = angle BDC = 20° (given angle C) and angle CBD = angle B (the vertex angle we want to find).
4. Use the triangle angle sum property: the sum of the interior angles of triangle BCD is 180°. So, write the equation: \( \angle C + \angle D + \angle B = 180^\circ \). Substitute the known values and expressions: \( 20^\circ + 20^\circ + x = 180^\circ \).
5. Solve the equation for \( x \) to find the measure of angle CBD (which is angle C B D).