https://file.aiquickdraw.com/mathbot/file/1727213240116vjryys5r.jpg

Let's break down the problem from the image you uploaded:

We are given:
1. \( \angle A \) is a supplement of \( \angle B \), meaning \( m\angle A + m\angle B = 180^\circ \).
2. \( \angle A \) is a complement of \( \angle C \), meaning \( m\angle A + m\angle C = 90^\circ \).
3. \( m\angle B = 124^\circ \).

We need to find \( m\angle B + m\angle C \).

### Step-by-step Solution:

1. From the first condition, \( \angle A \) is a supplement of \( \angle B \), we can write:
   \[
   m\angle A + m\angle B = 180^\circ
   \]
   Substituting \( m\angle B = 124^\circ \):
   \[
   m\angle A + 124^\circ = 180^\circ
   \]
   Solving for \( m\angle A \):
   \[
   m\angle A = 180^\circ - 124^\circ = 56^\circ
   \]

2. From the second condition, \( \angle A \) is a complement of \( \angle C \), so:
   \[
   m\angle A + m\angle C = 90^\circ
   \]
   Substituting \( m\angle A = 56^\circ \):
   \[
   56^\circ + m\angle C = 90^\circ
   \]
   Solving for \( m\angle C \):
   \[
   m\angle C = 90^\circ - 56^\circ = 34^\circ
   \]

3. Finally, to find \( m\angle B + m\angle C \):
   \[
   m\angle B + m\angle C = 124^\circ + 34^\circ = 158^\circ
   \]

### Final Answer:
\[
m\angle B + m\angle C = 158^\circ
\]

Let me know if you'd like any further details or explanations!

Here are 5 related questions to expand your understanding:
1. What is the difference between complementary and supplementary angles?
2. How do you find the third angle of a triangle if two angles are given?
3. Can two angles be both complementary and supplementary? Why or why not?
4. How does the sum of interior angles in a polygon change with the number of sides?
5. What happens if two angles are both supplementary and equal?

**Tip:** Always double-check angle relationships to ensure the correct use of definitions (complementary and supplementary).

∠A is a supplement of ∠B, ∠A is a complement of ∠C, and m∠B = 124°. Find m∠B + m∠C.

Solve the problem where ∠A is both a supplement to ∠B and a complement to ∠C, with m∠B given as 124°. This solution involves applying the properties of supplementary and complementary angles. Ideal for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation