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which are the correct measures for <dce and <cab?
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a. <dce = 61°, <cab = 61°
b. <dce = 61°, <cab = 55°
c. <dce = 55°, <cab = 61°
d. <dce = 55°, <cab = 64°

Explanation:

Step1: Find measure of ∠DCE

∠DCE and the 125 - degree angle are supplementary (linear - pair). So, ∠DCE=180° - 125° = 55°.

Step2: Find measure of ∠CAB

In triangle ABC, we know one angle ∠B = 64° and using the angle - sum property of a triangle (sum of angles in a triangle is 180°). Let ∠CAB=x. Then x + 64°+ (180° - 125°)=180°. Simplifying, x+64° + 55°=180°, x=180°-(64° + 55°)=61°.

Answer:

c. ∠DCE = 55°, ∠CAB = 61°