https://file.aiquickdraw.com/mathbot/file/1729704177958pghja4ft.jpg

From the image, we see a triangle \( \triangle STU \) that includes angle \( \angle ESU = 150^\circ \), a right angle at \( \angle TUS \), and we are tasked with solving for \( x \) (likely the measure of angle \( \angle STU \)).

To solve this, we can use the fact that the sum of angles in a triangle is always \( 180^\circ \).

1. Given that \( \angle TUS = 90^\circ \), and \( \angle ESU = 150^\circ \) corresponds to the exterior angle (complementary to \( \angle STU \)).
   
2. To find \( \angle STU \), we first calculate the interior angle \( \angle SUU \) from the exterior angle:
   \[
   \angle SUU = 180^\circ - 150^\circ = 30^\circ
   \]

3. Now, using the triangle angle sum property:
   \[
   \angle STU + 30^\circ + 90^\circ = 180^\circ
   \]
   Simplifying:
   \[
   \angle STU = 180^\circ - 120^\circ = 60^\circ
   \]

Thus, \( x = 60^\circ \).

Would you like more details on this solution or have any further questions?

Here are five related questions:
1. How do you calculate the exterior angle of a triangle?
2. What is the relationship between complementary and supplementary angles?
3. How can you find missing angles in different types of triangles?
4. What is the angle sum property of polygons in general?
5. How can trigonometric ratios be applied in right triangles?

**Tip**: Always double-check whether the given angles are interior or exterior when dealing with geometric figures!

Solve for the angle x in triangle STU, where angle ESU is 150 degrees, and angle TUS is a right angle.

Learn how to solve for the angle x in triangle STU, given a 150-degree exterior angle ESU and a right angle TUS. This geometry problem explores key concepts like the triangle angle sum property and exterior angles. Suitable 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