Help me find the Angle

Find Angle ECB

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Step 1) Find angle EDC. This is the missing acute angle of the right triangle. Let's call this angle x for now. This angle x adds to the other acute angle (31) to get 90, so 31+x = 90 which solves to x = 59 when you subtract 31 from both sides.

Step 2) Add angles EDC and ADE to get 59+60 = 119. So angle ADC is 119 degrees.

Step 3) Using the idea that adjacent angles of a parallelogram are supplementary, we add adjacent angles ADC and BCD to get 180. Let y be the measure of angle BCD. So we have 119+y = 180 which solves to y = 61

Step 4) Let z be the measure of angle ECB. This adds to angle ECD = 31 to get the measure of angle BCD. So, z+31 = 61 solves to z = 30

Check out the diagram below.

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