angles of a triangle (textbook pgs. 335 - 338)
6.1 the acute angles of a right triangle are complementary
abbreviation: acute ∠s of a rt △ are comp.
example: if ∠c is a right angle, then ∠a and ∠b are complementary. ( mangle a + mangle b = 90^circ )
1.
triangle ( abc ) with right angle at ( c ), ( angle b = 37^circ ), find ( mangle a ):
2.
triangle ( abc ) with right angle at ( c ), ( angle a = 32^circ ), find ( mangle b ):
3.
triangle ( abc ) with right angle at ( c ), ( angle a = 50.1^circ ), find ( mangle b ):
4.
triangle ( abc ) with right angle at ( c ), ( angle b = 60^circ ), find ( mangle a ):
5.
triangle ( abc ) with right angle at ( c ), ( angle a = 41^circ ), find ( mangle b ):
6.
triangle ( abc ) with right angle at ( c ), ( angle b = 87^circ ), find ( mangle a ):
7.
triangle ( abc ) with right angle at ( c ), ( angle b = 37^circ ), find ( mangle a ):
8.
triangle ( abc ) with right angle at ( c ), ( angle a = 47^circ ), find ( mangle b ):

Question

Accepted Answer

### Problem 1:
# Explanation:
## Step1: Recall the property (acute angles in a right triangle are complementary, so $ m\angle A + m\angle B = 90^\circ $). Here, $ m\angle B = 37^\circ $.
## Step2: Solve for $ m\angle A $: $ m\angle A = 90^\circ - 37^\circ = 53^\circ $.
# Answer: $ 53^\circ $

### Problem 2:
# Explanation:
## Step1: Use the complementary angles property ($ m\angle A + m\angle B = 90^\circ $). Given $ m\angle A = 32^\circ $.
## Step2: Calculate $ m\angle B $: $ m\angle B = 90^\circ - 32^\circ = 58^\circ $.
# Answer: $ 58^\circ $

### Problem 3:
# Explanation:
## Step1: Apply the complementary angles rule ($ m\angle A + m\angle B = 90^\circ $). Here, $ m\angle A = 50.1^\circ $.
## Step2: Find $ m\angle B $: $ m\angle B = 90^\circ - 50.1^\circ = 39.9^\circ $.
# Answer: $ 39.9^\circ $

### Problem 4:
# Explanation:
## Step1: Use the complementary angles property ($ m\angle A + m\angle B = 90^\circ $). Given $ m\angle B = 60^\circ $.
## Step2: Solve for $ m\angle A $: $ m\angle A = 90^\circ - 60^\circ = 30^\circ $.
# Answer: $ 30^\circ $

### Problem 5:
# Explanation:
## Step1: Recall the complementary angles rule ($ m\angle A + m\angle B = 90^\circ $). Given $ m\angle A = 41^\circ $.
## Step2: Calculate $ m\angle B $: $ m\angle B = 90^\circ - 41^\circ = 49^\circ $.
# Answer: $ 49^\circ $

### Problem 6:
# Explanation:
## Step1: Apply the complementary angles property ($ m\angle A + m\angle B = 90^\circ $). Given $ m\angle B = 87^\circ $.
## Step2: Find $ m\angle A $: $ m\angle A = 90^\circ - 87^\circ = 3^\circ $.
# Answer: $ 3^\circ $

### Problem 7:
# Explanation:
## Step1: Use the complementary angles rule ($ m\angle A + m\angle B = 90^\circ $). Given $ m\angle B = 37^\circ $.
## Step2: Solve for $ m\angle A $: $ m\angle A = 90^\circ - 37^\circ = 53^\circ $.
# Answer: $ 53^\circ $

### Problem 8:
# Explanation:
## Step1: Apply the complementary angles property ($ m\angle A + m\angle B = 90^\circ $). Given $ m\angle A = 47^\circ $.
## Step2: Calculate $ m\angle B $: $ m\angle B = 90^\circ - 47^\circ = 43^\circ $.
# Answer: $ 43^\circ $

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QUESTION IMAGE

Question

Explanation:

Problem 1:

Step1: Recall the property (acute angles in a right triangle are complementary, so \( m\angle A + m\angle B = 90^\circ \)). Here, \( m\angle B = 37^\circ \).

Step2: Solve for \( m\angle A \): \( m\angle A = 90^\circ - 37^\circ = 53^\circ \).

Step1: Use the complementary angles property (\( m\angle A + m\angle B = 90^\circ \)). Given \( m\angle A = 32^\circ \).

Step2: Calculate \( m\angle B \): \( m\angle B = 90^\circ - 32^\circ = 58^\circ \).

Step1: Apply the complementary angles rule (\( m\angle A + m\angle B = 90^\circ \)). Here, \( m\angle A = 50.1^\circ \).

Step2: Find \( m\angle B \): \( m\angle B = 90^\circ - 50.1^\circ = 39.9^\circ \).

Answer:

Problem 2: