In right triangle $ABC$, angle $BAC$ measures $56°$. What is the measure of angle $BDC$ if $D$ is a point on $AC$ such that $BD$ is perpendicular to $AC$?

• A. $56°$
• B. $112°$
• C. $34°$
• D. $28°$

Answer: (C)

Verified step by step guidance

1. Identify the given information: triangle ABC is a right triangle, and angle BAC measures 56°.
2. Recall that the sum of angles in any triangle is 180°. Since ABC is a right triangle, one angle is 90°, and angle BAC is 56°, so find angle ABC by subtracting these from 180° using the formula: \$180^\circ - 90^\circ - 56^\circ$.
3. Point D lies on segment AC such that BD is perpendicular to AC. This means triangle BDC is a right triangle with right angle at D.
4. Since BD is perpendicular to AC, angle BDC is 90°. To find angle BDC, consider triangle BDC and use the fact that the angles in triangle BDC sum to 180°.
5. Use the known angles and relationships to express angle BDC in terms of the given angles, and solve for the measure of angle BDC.