Chapter 2: Q. 201 (page 144)

The angles in a triangle are
such that one angle is twice the
smallest angle, while the third
angle is three times as large as the
smallest angle. Find the measures
of all three angles.

Short Answer

Expert verified

The three angles measures $30 °, 60 ° a n d 90 °$ .

Step by step solution

Given information:

Let the smallest angle $∠ A$ be $a °$ ,

then the second angle $∠ B$ be $2 a °$

and the third angle $∠ C$ be $3 a °$

Step 2:

Formula: $∠ A + ∠ B + ∠ C = 180 °$

Step 3:

Substitute: $a ° + 2 a ° + 3 a ° = 180 °$

Step 4:

On solving:

$6 a ° = 180 ° a ° = 30 °$

Step 5:

From Step 1:

$∠ A = a ° = 30 ° ∠ B = 2 a ° = 2 \times 30 ° = 60 ° ∠ C = 3 a ° = 3 \times 30 ° = 90 °$

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The angles in a triangle are
such that one angle is twice the
smallest angle, while the third
angle is three times as large as the
smallest angle. Find the measures
of all three angles.

Short Answer

Step by step solution

Given information:

Step 2:

Step 3:

Step 4:

Step 5:

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The angles in a triangle aresuch that one angle is twice thesmallest angle, while the thirdangle is three times as large as thesmallest angle. Find the measuresof all three angles.

Short Answer

Step by step solution

Given information:

Step 2:

Step 3:

Step 4:

Step 5:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Geometry

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Discrete Mathematics

Study anywhere. Anytime. Across all devices.

The angles in a triangle are
such that one angle is twice the
smallest angle, while the third
angle is three times as large as the
smallest angle. Find the measures
of all three angles.