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Answer:

20 degrees.

Step-by-step explanation:

We can assign variables for this problem. We can see that the overall angle adds up to 100 degrees, with Angle 1 being four times Angle 2, where Angle 2 being a random variable we can call x.

Using this information, we can conclude that Angle 1 is 4x and Angle 2 is x.

We can add those variables together, equal it to 100 degrees since ABD is known to be 100 degrees, to find variable x, and input it to find angle 2.

4x+x=100          (make equation)

5x=100              (add like terms)

x=20                  (isolate x)

We know that x stands for 20, and since angle 2 is just x, the answer is just 20 degrees.

The value of m∠2 is 20°

m∠ABD = 100°

m∠1 and m∠2 are adjacent angles.

Adjacent angles:

Adjacent angles are angles that have common vertex

m∠1 is four times m∠2. Therefore,

m∠1 =  4(m∠2)

100° = m∠1  + m∠2

Therefore,

100 = 4(m∠2) + m∠2

100 = 5(m∠2)

divide both sides by 5

100 / 5 = m∠2

m∠2 = 20°

Therefore,

m∠1 = 100 - 20 = 80°

learn more on angles here: https://brainly.com/question/10403348?referrer=searchResults

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