https://file.aiquickdraw.com/mathbot/file/1727366162376edi9gx6n.jpg

To solve for angle \( p \), we can use the fact that the angles inside any triangle always add up to 180°.

### Step 1: Calculate the exterior angle
The pink angle, marked as 278°, is an exterior angle, which is supplementary to the interior angle of the triangle at the same vertex. Since supplementary angles add up to 360°:
\[
\text{Interior angle} = 360^\circ - 278^\circ = 82^\circ
\]

### Step 2: Use the sum of angles in a triangle
Now that we know two of the angles inside the triangle (82° and 126°), we can find the third angle, \( p \), using the equation:
\[
p + 82^\circ + 126^\circ = 180^\circ
\]
\[
p + 208^\circ = 180^\circ
\]
\[
p = 180^\circ - 208^\circ = -28^\circ
\]

This result is negative, which indicates an inconsistency in the angle configuration of this diagram. The angle sum of the given data surpasses 180°, which suggests a misinterpretation in labeling or drawing.

Would you like further clarification or assistance with this problem?

Here are 5 related questions to explore this concept:

1. What are supplementary angles, and how are they used in geometry?
2. Can the sum of a triangle's angles ever exceed 180°?
3. How do exterior and interior angles relate to each other in polygons?
4. What methods can be used to check if an angle is calculated correctly?
5. What is the role of congruency in triangle geometry problems?

**Tip:** Always double-check the given angle values in problems involving triangles to ensure they align with the fundamental properties (like the sum of 180°).

Find angle p. Given the other two angles in the triangle are 278° (exterior) and 126° (interior).

Learn how to solve for angle p in a triangle where one angle is 126° and the exterior angle is 278°. This problem covers key geometric concepts such as the triangle angle sum theorem and supplementary angles. Suitable for students in 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