Chapter 2: Q. 200 (page 144)

The measure of the smallest
angle of a right triangle is 20°
less than the measure of the next
larger angle. Find the measures of
all three angles.

Short Answer

Expert verified

The three angles measures $35 °, 55 ° a n d 90 °$ .

Step by step solution

Given information:

Let the larger angle $∠ A$ be $a °$ ,

then the smallest angle $∠ B$ will be $a ° - 20 °$ .

Also, third angle $∠ C$ is $90 °$ (Right triangle)

Step 2:

Formula: $∠ A + ∠ B + ∠ C = 180 °$

Step 3:

Substitute: $a ° + (a ° - 20 °) + 90 ° = 180 °$

Step 4:

On solving:

$2 a ° + 70 ° = 180 ° 2 a ° = 180 ° - 70 ° 2 a ° = 110 ° a ° = \frac{110 °}{2} = 55 °$

Step 5:

From Step 1, Given $∠ A = a ° = 55 °$

$∠ B = a ° - 20 ° = 55 ° - 20 ° = 35 °$ .

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The measure of the smallest
angle of a right triangle is 20°
less than the measure of the next
larger 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 measure of the smallestangle of a right triangle is 20°less than the measure of the nextlarger angle. Find the measures ofall 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

Mechanics Maths

Decision Maths

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

The measure of the smallest
angle of a right triangle is 20°
less than the measure of the next
larger angle. Find the measures of
all three angles.