The sum of two complementary angles is 90°. For one pair of complementary angles, the measure of the first angle is 15 less than twice the measure of the second angle. Write a system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b.
2 answers:
let 2nd angle = x
then 1st angle = 2x-15
then you have 90 = x + 2x-15
2x +x = 3x
so now 90 = 3x-15
add 15 to each side
105=3x
x = 105/3 = 35
1st angle = 35 degrees
2nd angle = 2(35) - 15 = 70-15 = 65
Answer:
Measure of first angle = 65° and Measure of second angle = 35°
Step-by-step explanation:
Let measure of first angle be a and measure of second angle be b
Now, the measure of the first angle is 15 less than twice the measure of the second angle
⇒ a + 15 = 2b
⇒ a = 2b - 15
Now, sum of two complementary angles is 90
⇒ a + b = 90
⇒ 2b - 15 + b = 90
⇒ 3b - 15 = 90
⇒ 3b = 105
⇒ b = 35
And a = 65
Therefore, Measure of first angle = 65° and Measure of second angle = 35°
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