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vitfil [10]
3 years ago
6

Analyze Mathematical Relationships (1)(F) Suppose the measures of ∠1 and ∠2 are in a 4 ∶ 11 ratio. Find their measures. (Diagram

is not to scale.)
Mathematics
1 answer:
Gekata [30.6K]3 years ago
4 0

If the angles are complementary, we have that:

  • The measure of angle 1 is of 24º.
  • The measure of angle 2 is of 66º.

-----------------

  • If two angles are complementary, the <u>sum of their measures is 90º.</u>
  • In this problem, we suppose that angles 1 and 2 are complementary, thus:

m_1 + m_2 = 90

-----------------

  • The measures of angle 1 and angle 2 are in a 4:11 ratio, thus:

m_1 = \frac{4}{4+11} = \frac{4}{15}(m_1 + m_2)

m_2 = \frac{11}{4+11} = \frac{11}{15}(m_1 + m_2)

-----------------

Considering m_1 + m_2 = 90

m_1 = \frac{4}{15}(m_1 + m_2) = \frac{4}{15} \times 90 = 4 \times 6 = 24

m_2 = \frac{11}{15}(m_1 + m_2) = \frac{11}{15} \times 90 = 11 \times 6 = 66

The measure of angle 1 is of 24º.

The measure of angle 2 is of 66º.

A similar problem is given at brainly.com/question/24738896

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