If the angles are complementary, we have that:
- The measure of angle 1 is of 24º.
- The measure of angle 2 is of 66º.
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- If two angles are complementary, the sum of their measures is 90º.
- In this problem, we suppose that angles 1 and 2 are complementary, thus:
[tex]m_1 + m_2 = 90[/tex]
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- The measures of angle 1 and angle 2 are in a 4:11 ratio, thus:
[tex]m_1 = \frac{4}{4+11} = \frac{4}{15}(m_1 + m_2)[/tex]
[tex]m_2 = \frac{11}{4+11} = \frac{11}{15}(m_1 + m_2)[/tex]
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Considering [tex]m_1 + m_2 = 90[/tex]
[tex]m_1 = \frac{4}{15}(m_1 + m_2) = \frac{4}{15} \times 90 = 4 \times 6 = 24[/tex]
[tex]m_2 = \frac{11}{15}(m_1 + m_2) = \frac{11}{15} \times 90 = 11 \times 6 = 66[/tex]
The measure of angle 1 is of 24º.
The measure of angle 2 is of 66º.
A similar problem is given at https://brainly.com/question/24738896
