Final answer:
To find the measure of angle BDC, use the angle sum property of triangles. Angle BDC has a measure of 174°.
Step-by-step explanation:
To find the measure of angle BDC, we can use the given information and apply the angle sum property of triangles:
Since m angle A = 84° and m angle 3 = m angle 4, we know that m angle 3 = 84°. Therefore, angle 3 and angle 4 are each 84°.
Since m angle 1 = m angle 2, we know that angle 1 and angle 2 are congruent. By the angle sum property of triangles, angle 1 + angle 2 = 180°. So, angle 1 = angle 2 = 180°/2 = 90°. Since angle 3 = angle 4 = 84°, the sum of angle 1 and angle 3 is 90° + 84° = 174°. Therefore, angle BDC has a measure of 174°.