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Answer:

m < 1 = 18°

Step-by-step explanation:

If <ABD = 72°, and m < 2 is three times the measure of m < 1, then:

Let < ABC = m < 1 =  x

     < CBD = m < 2 = 3x

We can set up the following formula, since the sum of the measures of angles < 1 and < 2 is equal to <ABD (72°):

m < 1 + m < 2 = < ABD

x + 3x = 72°

Add like terms:

4x = 72°

Divide both sides by 4 to solve for x:

[tex]\frac{4x}{4} = \frac{72}{4}[/tex]

x = 18

Since x = 18, and m < 1 = x , then m < 1 = 18°.

And since m < 2 = 3x, then m < 2 = 3(18°) = 54°.

Let's check to see whether we derived the correct answers by plugging in the values of m < 1 and m < 2 into the established formula:

m < 1 + m < 2 = < ABD

18° + 54° = 72°

72° = 72° (True statement).

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