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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