Answer:
41° and 49°
Step-by-step explanation:
Given:
Angle 1 and angle 2 are complementary angles.
The measures of angle 1 is 8 more than the measure of angle 2.
Question asked:
Determine the measures of angle 1 and 2.
Solution:
Let ∠1 = [tex]x[/tex]
Then ∠2 = [tex]x+8[/tex] (given)
As we know that sum of complementary angles are 90° and here given that angle 1 and angle 2 are complementary angles which means,
∠1 + ∠2 = 90°
[tex]x+x+8=90[/tex]°
[tex]2x +8=90[/tex]°
Subtracting both sides by 8,
[tex]2x=90[/tex]°[tex]-8[/tex]
[tex]2x = 82[/tex]°
Dividing both sides by 2,
[tex]x=41[/tex]°
∠1 = [tex]x=41[/tex]°
∠2 = [tex]x+8[/tex]
∠2 = [tex]41+8[/tex] = 49°
Therefore, the measures of angle 1 and 2 are 41° and 49°
