Question

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.)

Answer 1

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:

$m_1 + m_2 = 90$

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

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

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

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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