https://file.aiquickdraw.com/mathbot/file/1728332853713xllp48i8.jpg

The triangle in the image is an isosceles triangle, meaning two sides are equal in length, and the two base angles are also equal. In this case, \( \triangle QRS \) has \( \angle Q = 40^\circ \), and angles \( \angle R \) and \( \angle S \) must be equal since it's an isosceles triangle.

Using the fact that the sum of the interior angles of any triangle is \( 180^\circ \), we can set up the following equation:

\[
\angle Q + \angle R + \angle S = 180^\circ
\]
\[
40^\circ + 2x = 180^\circ
\]
\[
2x = 140^\circ
\]
\[
x = 70^\circ
\]

Thus, \( \angle R = 70^\circ \) and \( \angle S = 70^\circ \).

The correct answer is **C**: \( \angle R = 70^\circ \) and \( \angle S = 70^\circ \).

Would you like further details or have any questions?

Here are 5 related questions:
1. Why do the angles of any triangle always sum up to \(180^\circ\)?
2. How do you determine if a triangle is isosceles based on its angles?
3. If \( \angle Q \) was \(50^\circ\) instead, how would you calculate \( \angle R \) and \( \angle S \)?
4. What are the properties of an equilateral triangle compared to an isosceles triangle?
5. Can an isosceles triangle have an obtuse angle? How would you identify that?

**Tip:** Always remember that the sum of the angles in any triangle is \(180^\circ\), which is crucial in solving angle-related problems.

Based on the information given, what are the measures of ∠R and ∠S?

Solve for the measures of ∠R and ∠S in an isosceles triangle where ∠Q is 40°. Learn how to apply the Angle Sum Theorem and the properties of an isosceles triangle. 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