# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-6/12

Exercises: Try Out - Set 6: Real exam simulation to sharpen your skills and build confidence. - Problem 12

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## Exercise 12

### Question

export const metadata = {
  title: "Problem 12",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

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

The value of <InlineMath math="a" /> in the figure below is ...

<Graph title="Triangle" description="Geometric illustration with labeled angles." />


### Choices

- [x] $$20^\circ$$
- [ ] $$30^\circ$$
- [ ] $$40^\circ$$
- [ ] $$50^\circ$$
- [ ] $$80^\circ$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 12",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

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

<Graph title="Triangle" description="Geometric illustration with labeled angles." />

Consider the small triangle at the bottom. The sum of angles in a triangle is <InlineMath math="180^\circ" />. Given the top vertex angle is <InlineMath math="100^\circ" />. So, the sum of the two base angles is:

<MathContainer>
  <BlockMath math="x + y = 180^\circ - 100^\circ = 80^\circ" />
</MathContainer>

Next, consider the large triangle. Its base angles are <InlineMath math="(x+y)" /> and <InlineMath math="(y+x)" />. Since <InlineMath math="x+y = 80^\circ" />, both base angles of the large triangle are <InlineMath math="80^\circ" />. The sum of angles in the large triangle is <InlineMath math="180^\circ" />:

<MathContainer>
  <BlockMath math="a + (x+y) + (y+x) = 180^\circ" />
  <BlockMath math="a + 80^\circ + 80^\circ = 180^\circ" />
  <BlockMath math="a + 160^\circ = 180^\circ" />
  <BlockMath math="a = 20^\circ" />
</MathContainer>

Thus, the value of <InlineMath math="a" /> is <InlineMath math="20^\circ" />.


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