Answer:
m₁ = 53° and its complement m₂ = 37°
Step-by-step explanation:
To solve this problem, we'll explore the relationship between an angle and its complement, and then use algebra to find the specific measurements.
Firstly, we know that complementary angles add up to 90 degrees. Let's denote the measure of the angle as 'm₁' and its complement as 'm₂'. Thus, we can create an equation:
⇒ m₁ + m₂ = 90° ...(1)
The question states that 'm₁' is 21 degrees less than twice the measurement of its complement. Mathematically, this can be expressed as:
⇒ m₁ = 2m₂ - 21° ...(2)
Therefore, we have a system of equations with two unknowns. Substitute equation (2) into equation (1) and solve for 'm₂':
⇒ (2m₂ - 21°) + m₂ = 90°
⇒ 2m₂ - 21° + m₂ = 90°
⇒ 3m₂ - 21° = 90°
⇒ 3m₂ - 21° = 90°
⇒ 3m₂ = 111°
∴ m₂ = 111°/3 = 37°
Thus, m₂ = 37°. Take this value and plug it into equation (1) to find 'm₁':
⇒ m₁ + 37° = 90°
∴ m₁ = 53°
So, the measures of the angles are m₁ = 53° and its complement m₂ = 37°.
