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3 years ago

22. The measures of the angles of ADEF are in the ratio 2:4:4. What are the

Mathematics

1 answer:

denis23 [38]3 years ago

3 0

The measures of the angles of Δ DEF are 36° , 72° , 72°

Step-by-step explanation:

The sum of the measures of the interior angles in any triangle is 180°

In Δ DEF

The ratio between the measures of its interior angles is 2 : 4 : 4

To find the measure of each angle

1. Find the sum of the ratio between the measures of its angles

2. Divide 180° by the sum of the ratio

3. Multiply the quotient by each ratio

∵ The ratio between the measures of the angles of Δ DEF = 2 : 4 : 4

∴ The sum of the ratio = 2 + 4 + 4 = 10

→ m∠D : m∠E : m∠F : sum of the ratio

→ 2 : 4 : 4 : 10

→ ? : ? : ? : 180°

Divide 180 by 10, then multiply the quotient by the components of

the ratio to find the measure of each angle

∵ m∠D = $(2)\frac{180}{10}$

∴ m∠D = 36°

∵ m∠E = $(4)\frac{180}{10}$

∴ m∠D = 72°

∵ m∠F = $(4)\frac{180}{10}$

∴ m∠F = 72°

The measures of the angles of Δ DEF are 36° , 72° , 72°

Learn more:

You can learn more about the ratio in brainly.com/question/2707032

#LearnwithBrainly

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