Question

If mZABC is one degree less than three times mZABD and mZDBC = 47°, find each measure.

MZABD =
m ZABC =

Answer 1

To find the measures of mZABD and mZABC, we can use the given information. By setting up an equation and following the steps, we can find that mZABD measures 33.5° and mZABC measures 99.5°.

Step-by-step explanation:

To find the measure of mZABD and mZABC, we can use the given information.

First, we know that mZABC is one degree less than three times mZABD. So, we can write this as:

mZABC = 3 imes mZABD - 1

Next, we are given that mZDBC = 47°. Since ZDBC is a straight line, the sum of all the angles around it is 180°. Therefore, we can write:

mZABD + mZDBC + mZABC = 180°

Now, we can substitute the value of mZABC from the first equation:

mZABD + 47° + (3 imes mZABD - 1) = 180°

Simplifying the equation, we get:

4 imes mZABD + 46° = 180°

Subtracting 46° from both sides, we have:

4 imes mZABD = 134°

Dividing both sides by 4, we find:

mZABD = 33.5°

Finally, we can substitute this value back into the first equation to find mZABC:

mZABC = 3 imes 33.5° - 1 = 100.5° - 1 = 99.5°