Question

△ABC and △DCE are shown. Triangles ABC and DCE share point C. AB and BC are congruent, and CD and CE are congruent. Angle ABC is 92 degrees. What is m∠BAC?

a) 44 degrees
b) 46 degrees
c) 92 degrees
d) 134 degrees

Answer 1

To find m∠BAC in △ABC, knowing ∠ABC is 92 degrees and sides AB and BC are congruent, we used the triangle angle sum theorem. After doing the math, we determined that m∠BAC is a. 44 degrees.

Step-by-step explanation:

The student is asking about the measure of m∠BAC in a given geometric figure where △ABC and △DCE share a common point C, and certain sides of the triangles are congruent.

To find m∠BAC, we can use the fact that the sum of angles in a triangle is always 180 degrees. Since △ABC has one angle measuring 92 degrees (∠ABC) and it is given that AB and BC are congruent, the remaining two angles must be equal. Let x be the measure of the angle ∠BAC, so:

1. m∠ABC + 2x = 180° (sum of angles in a triangle is 180°)
2. 92° + 2x = 180°
3. 2x = 180° - 92°
4. 2x = 88°
5. x = 44°

Therefore, the measure of the angle BAC is 44 degrees, which corresponds to option (a).