# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-10/2

Exercises: Try Out - Set 10: Real exam simulation to sharpen your skills and build confidence. - Question 2

---

## Exercise 2

### Question

export const metadata = {
  title: "Question 2",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

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

<Graph
  title="Intersecting Angles"
  description={<>Determine the measure of angle <InlineMath math="z" /> in terms of <InlineMath math="x" />.</>}
/>

Based on the figure above, if <InlineMath math="x^\circ = y^\circ" />, what is the measure of angle <InlineMath math="z" /> in terms of <InlineMath math="x" />?


### Choices

- [ ] $$90 - x$$
- [ ] $$90 - 2x$$
- [ ] $$180 - x$$
- [x] $$180 - 2x$$
- [ ] Unknown

### Answer & Explanation

export const metadata = {
  title: "Solution for Question 2",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

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

<Graph
  id="question-2"
  title="Angle Analysis"
  description="Relationship between intersecting angles."
/>

From the figure, we can see that the angle vertically opposite to <InlineMath math="z^\circ" /> is the angle between the two diagonal lines at the top. The measure of that angle is equal to <InlineMath math="z^\circ" />.

Since the angles on a straight line sum to <InlineMath math="180^\circ" />, the sum of angle <InlineMath math="x^\circ" />, vertical angle <InlineMath math="z^\circ" />, and <InlineMath math="y^\circ" /> is <InlineMath math="180^\circ" />:

<MathContainer>
  <BlockMath math="x^\circ + z^\circ + y^\circ = 180^\circ" />
</MathContainer>

Given that <InlineMath math="x^\circ = y^\circ" />, we can substitute <InlineMath math="y" /> with <InlineMath math="x" />:

<MathContainer>
  <BlockMath math="x^\circ + z^\circ + x^\circ = 180^\circ" />
  <BlockMath math="z^\circ + 2x^\circ = 180^\circ" />
  <BlockMath math="z^\circ = 180^\circ - 2x^\circ" />
</MathContainer>

Therefore, the measure of angle <InlineMath math="z" /> is <InlineMath math="180 - 2x" />.


---