Answer:
m∠1 = 128°
m∠2 = 52°
Explanation:
We can find the measures of angles 1 and 2 using a system of equations, where:
- x represents the measure of ∠1,
- and y represents the measure of ∠2.
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First equation:
- Supplementary angles form straight angles.
- This means that the sum of supplementary angles is 180°.
Thus, our first equation is given by:
x + y = 180
Second equation:
Since m∠1 is 24° that 2 times m∠2, our second equation is given by:
x = 2y + 24
Method to solve: Substitution:
Solving for y (i.e., the measure of angle 2):
Now, we can solve for y by substituting 2y + 24 for x in first equation (i.e., x + y = 180):
2y + 24 + y = 180
(3y + 24 = 180) - 24
(3y = 156) / 3
y = 52
Therefore, the measure of angle 2 is 52°.
Solving for x (i.e., the measure of angle 1):
Now, we can solve for x by plugging in 52 for y in the first equation (i.e., x + y = 180):
(x + 52 = 180) - 52
x = 128
Therefore, the measure of angle 1 is 128°.