# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-9/3

Exercises: Try Out - Set 9: Real exam simulation to sharpen your skills and build confidence. - Problem 3

---

## Exercise 3

### Question

export const metadata = {
  title: "Problem 3",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

import { Graph } from "../graph";

<Graph
  title="Lines and Angles"
  description={
    <>
      Two parallel lines <InlineMath math="PQ" /> and <InlineMath math="RS" />{" "}
      cut by a zig-zag line forming angles <InlineMath math="25^\circ" />,{" "}
      <InlineMath math="135^\circ" />, and <InlineMath math="\alpha" />.
    </>
  }
/>

If <InlineMath math="PQ" /> is parallel to <InlineMath math="RS" />, then the value of <InlineMath math="\alpha" /> is...


### Choices

- [ ] $$45^\circ$$
- [ ] $$65^\circ$$
- [x] $$70^\circ$$
- [ ] $$75^\circ$$
- [ ] $$80^\circ$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 3",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/26/2025",
};

import { Graph } from "../graph";

<Graph
  mode="answer"
  title="Solution Visualization"
  description={
    <>
      Auxiliary line divides angle <InlineMath math="\alpha" /> into{" "}
      <InlineMath math="\beta" /> and <InlineMath math="\gamma" />.
    </>
  }
/>

We draw an auxiliary line parallel to lines <InlineMath math="PQ" /> and <InlineMath math="RS" /> passing through the vertex of angle <InlineMath math="\alpha" />.
This line divides angle <InlineMath math="\alpha" /> into two parts, <InlineMath math="\beta" /> and <InlineMath math="\gamma" />.

#### Finding the Value of <InlineMath math="\beta" />

Notice that angle <InlineMath math="\beta" /> and the <InlineMath math="25^\circ" /> angle are alternate interior angles.
Since the lines are parallel, their measures are equal:

<MathContainer>
  <BlockMath math="\beta = 25^\circ" />
</MathContainer>

#### Finding the Value of <InlineMath math="\gamma" />

Angle <InlineMath math="\gamma" /> and the <InlineMath math="135^\circ" /> angle are consecutive interior angles.
The sum of these two angles is <InlineMath math="180^\circ" />:

<MathContainer>
  <BlockMath math="\gamma + 135^\circ = 180^\circ" />
  <BlockMath math="\gamma = 180^\circ - 135^\circ = 45^\circ" />
</MathContainer>

#### Calculating the Value of <InlineMath math="\alpha" />

The value of <InlineMath math="\alpha" /> is the sum of <InlineMath math="\beta" /> and <InlineMath math="\gamma" />:

<MathContainer>
  <BlockMath math="\alpha = \beta + \gamma" />
  <BlockMath math="\alpha = 25^\circ + 45^\circ" />
  <BlockMath math="\alpha = 70^\circ" />
</MathContainer>

Therefore, the value of <InlineMath math="\alpha" /> is <InlineMath math="70^\circ" />.


---