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3. The measure of ZB is 33° more than half the measure of ZA.

a. If ZA and ZB are supplementary angles, then what are their measures?

User Leo Nix
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Answer:

If ZA and ZB are supplementary angles, then their measures add up to 180 degrees. So we can represent ZA as x and ZB as y.

According to the given information, the measure of ZB is 33° more than half the measure of ZA. So we can represent this as:

y = (1/2)x + 33

And since ZA and ZB are supplementary, we can express the relationship between the two angles as:

x + y = 180

Now we have a system of two equations with two variables:

y = (1/2)x + 33

x + y = 180

We can solve for x and y using these equations.

First, we substitute the first equation into the second equation:

x + ((1/2)x + 33) = 180

Simplifying:

x + (1/2)x + 33 = 180

x + (1/2)x = 180 - 33

x + (1/2)x = 147

Combining like terms:

(3/2)x = 147

Dividing both sides by 3/2

x = 98

Now we can substitute this value back into the first equation to find the measure of ZB:

y = (1/2)x + 33

y = (1/2)(98) + 33

y = 49 + 33

y = 82

So the measure of ZA is 98°, and the measure of ZB is 82°.

Explanation:

User Ankita Patel
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