Respuesta :
First, lets comprehend the question.
A complement of a number is a number in which added to the number, it will be measure 90.
The phrase: "More than" means you gotta add it
The phrase: "twice the complement of the number" means you gotta multiply the complement by 2.
Next step, solving.
To get the complement of 42° we must subtract it by 90°.
So 90-42=48. So the complement of 42 is 48 since they both add up to 90.
Now it says here to multiply the complement twice. So multiply 48 by 2
A complement of a number is a number in which added to the number, it will be measure 90.
The phrase: "More than" means you gotta add it
The phrase: "twice the complement of the number" means you gotta multiply the complement by 2.
Next step, solving.
To get the complement of 42° we must subtract it by 90°.
So 90-42=48. So the complement of 42 is 48 since they both add up to 90.
Now it says here to multiply the complement twice. So multiply 48 by 2
The measure of the complementary angle is 16°. Using the definition of complementary angles, the value is obtained.
What are complementary angles?
The two angles whose sum is equal to 90° are said to be complementary angles. I.e., a and b are two complementary angles, then ∠a + ∠b = 90°.
Finding the complementary angle from the given data:
Given that,
An angle measures 42 degrees more than twice the measure of its complement.
So, consider the required complementary angle as x
Then twice of the complementary angle = 2x
The angle measures 42 degrees more than the twice the measure of its complement = 2x + 42
So, the other angle is (2x + 42)°
Since we know that sum of the complementary angles = 90°
⇒ x + (2x+42) = 90°
⇒ 3x + 42 = 90°
⇒ 3x = 90 - 42
⇒ 3x = 48°
∴ x = 16°
Thus, the measure of its complementary angle is 16°.
And the other angle is 2x + 42 = 2(16) + 42 = 74°
So, angles 74° and 16° are complementary angles.
Learn more about complementary angles here:
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