Question

Which is a possible measure of DCA in the triangle below?

Answer 1

Answer:

70°

Step-by-step explanation:

The total angle in a triangle is 180°. The total angle in a straight line is 180°. From the image attached, the ∠DCA must be greater than 45° because ∠BCA is greater than 90°. This means that ∠DCA is not 36° or 38° or 40° but it is 70°.

Therefore ∠DCA = 70°.

∠BCA + ∠DCA = 180° (angle on a straight line)

∠BCA = 180 - ∠DCA = 180 - 70 = 110°

∠BCA  + ∠BAC + 40 = 180° (angle in a triangle)

∠BAC = 180 - 110 - 40 = 30°