https://file.aiquickdraw.com/mathbot/file/1725594385695b5i9jgu0.jpg

In the given image, we have the following angles:

1. \( x^\circ \) is the angle adjacent to the \( 50^\circ \) angle and a right angle.
2. \( y^\circ \) is the exterior angle between the line and the \( 74^\circ \) angle.

### Step-by-step solution:

#### For \( x^\circ \):
The three angles on a straight line add up to 180°. So we can write the equation:
\[
x^\circ + 50^\circ + 90^\circ = 180^\circ
\]
Now, solving for \( x^\circ \):
\[
x^\circ = 180^\circ - 140^\circ = 40^\circ
\]

#### For \( y^\circ \):
We know that \( y^\circ \) is the exterior angle formed with the interior \( 74^\circ \) angle and the straight line. Since the straight angle is 180°, we can write:
\[
y^\circ + 74^\circ = 180^\circ
\]
Solving for \( y^\circ \):
\[
y^\circ = 180^\circ - 74^\circ = 106^\circ
\]

### Final answers:
- \( x^\circ = 40^\circ \)
- \( y^\circ = 106^\circ \)

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the sum of all interior angles on a straight line?
2. How can we calculate an unknown angle in a triangle using two known angles?
3. What are supplementary angles, and how do they relate to this problem?
4. Can an angle exceed 180°, and what is the term for such angles?
5. How do complementary angles differ from supplementary angles?

**Tip**: Always check for right angles in diagrams, as they simplify angle calculations.

In the given image, solve for x° and y°, where x° is adjacent to 50° and a right angle, and y° is the exterior angle formed by the line and the 74° angle.

This page provides a detailed step-by-step solution to find the unknown angles x° and y° in a geometric diagram. The problem uses the sum of angles on a straight line and the exterior angle theorem, with values x° = 40° and y° = 106°. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation