The sum of the measures of ∠𝐴 and ∠𝐵 is 90∘. The sum of the measures of ∠𝐴 and ∠𝐶 is 180∘. The sum of the measures of ∠𝐵 and ∠𝐷 is 180∘. What is the sum of the measures of ∠𝐶 and

∠𝐷?

Step 1: From the given information, we know that ∠A + ∠B = 90° and ∠A + ∠C = 180°.

Step 2: Subtract the first equation from the second to find the measure of ∠C. This gives us ∠C = 180° - 90° = 90°.

Step 3: We also know that ∠B + ∠D = 180°. Since ∠B = 90° - ∠A, we can substitute this into the equation to find ∠D. This gives us ∠D = 180° - ∠B = 180° - (90° - ∠A) = 90° + ∠A.

Step 4: To find the sum of the measures of ∠C and ∠D, we add the measures we found in steps 2 and 3. This gives us ∠C + ∠D = 90° + (90° + ∠A) = 180° + ∠A.

So, the sum of the measures of ∠C and ∠D is 180° + ∠A.

∠𝐷?

Step 1: From the given information, we know that ∠A + ∠B = 90° and ∠A + ∠C = 180°.

Step 2: Subtract the first equation from the second to find the measure of ∠C. This gives us ∠C = 180° - 90° = 90°.

Step 3: We also know that ∠B + ∠D = 180°. Since ∠B = 90° - ∠A, we can substitute this into the equation to find ∠D. This gives us ∠D = 180° - ∠B = 180° - (90° - ∠A) = 90° + ∠A.

Step 4: To find the sum of the measures of ∠C and ∠D, we add the measures we found in steps 2 and 3. This gives us ∠C + ∠D = 90° + (90° + ∠A) = 180° + ∠A.

So, the sum of the measures of ∠C and ∠D is 180° + ∠A.