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4 years ago

Three adjacent angles are at a point. The ratio of the measurements is 3:4:5. The angles should add to 360.

Mathematics

1 answer:

zheka24 [161]4 years ago

6 0

Answer:

90 degrees, 120 degrees and 150 degrees

Step-by-step explanation:

Given that three adjacent angles are at a point. The ratio of the measurements is 3:4:5. The angles should add to 360.

First add up all the ratio

3 + 4 + 5 = 12

For ratio 3

3/12 × 360 = 90 degree

For ratio 4

4/12 × 360 = 120 degree

For ratio 5

5/12 × 360 = 150 degree

90 + 120 + 150 = 360 degree.

The angles are therefore, 90 degrees, 120 degrees and 150 degrees

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In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that applym∠R > 90°

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Answer: The correct statements are,

m∠R > 90°

m∠S + m∠T < 90°

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Step-by-step explanation:

Here, RST is a triangle,

Therefore, m∠R+m∠S+m∠T = 180° ⇒ m∠S+m∠T = 180° - m∠R

Given: m∠R > m∠S + m∠T

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⇒ 180°- m∠R < 180° - (m∠S + m∠T) (by adding 180° on both sides)

⇒ m∠S+m∠T < 180° - (m∠S + m∠T)

⇒ m∠S+m∠T+ m∠S+m∠T < 180° ( by adding m∠S + m∠T on both sides)

⇒ 2(m∠S+m∠T) < 180°

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Again, m∠R > m∠S + m∠T

⇒ m∠R > m∠S and m∠R > m∠T

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And, there are not enough information to prove m∠S > m∠T

That is why m∠S > m∠T is also incorrect.

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See attachment for graph.

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