https://file.aiquickdraw.com/mathbot/file/172946921133249ddbjth.jpg

In the diagram, you are given two straight lines, \( PRT \) and \( QRS \), and a few angles. Specifically, you are provided the following information:

1. \( \angle PRS = 50^\circ \)
2. \( \angle QRT = 95^\circ \)
3. \( \angle RTS = x^\circ \)

To solve for \( x \), let's apply the following steps:

### Step 1: Use the fact that \( \angle QRT \) and \( \angle SRT \) are supplementary
Since \( QRS \) is a straight line, we know that:
\[
\angle QRT + \angle SRT = 180^\circ
\]
Given that \( \angle QRT = 95^\circ \), we can find \( \angle SRT \):
\[
95^\circ + \angle SRT = 180^\circ
\]
\[
\angle SRT = 180^\circ - 95^\circ = 85^\circ
\]

### Step 2: Use the sum of angles in \( \triangle RTS \)
In \( \triangle RTS \), the sum of the internal angles must be \( 180^\circ \). Therefore, we have:
\[
\angle RTS + \angle SRT + \angle RST = 180^\circ
\]
We already know \( \angle RTS = x^\circ \) and \( \angle SRT = 85^\circ \), and \( \angle RST = 50^\circ \) is given. Plugging in these values:
\[
x + 85^\circ + 50^\circ = 180^\circ
\]
\[
x + 135^\circ = 180^\circ
\]
\[
x = 180^\circ - 135^\circ = 45^\circ
\]

Thus, the value of \( x \) is \( \boxed{45^\circ} \).

### Final Answer:
The correct answer is \( \boxed{B} \).

Would you like further clarification or details on any steps?

---

Here are 5 related questions to practice:

1. If \( \angle QRT \) was 100°, what would \( x \) be?
2. How do you calculate exterior angles in triangles?
3. What is the sum of the interior angles of a quadrilateral?
4. In any triangle, how can you determine the third angle if you have two?
5. What are supplementary angles, and how are they applied in straight-line geometry?

**Tip:** Always remember that the sum of angles in a triangle is \( 180^\circ \). This rule is fundamental in many geometry problems!

In the diagram, PRT and QRS are straight lines. Given angles PRS = 50°, QRT = 95°, and RTS = x, find the value of x.

Learn how to solve for x in a geometric figure where PRT and QRS are straight lines. Apply the concept of supplementary angles and the sum of angles in a triangle to find the correct value of x. 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