The angles of a triangle are in ratio 4 ∶ 3 ∶ 2, what will be the supplementary of the largest angle of the triangle?
The angles of a triangle are in ratio 4 ∶ 3 ∶ 2, what will be the supplementary of the largest angle of the triangle?
A60°
B80°
C90°
D100°
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Correct Answer: [d] 100°
Explanation:
The angles of a triangle are given in the ratio 4:3:2. Let the common multiplier be \( x \) Therefore, the angles can be expressed as \( 4x \), \( 3x \), and \( 2x \)
The sum of the angles in a triangle is \( 180^\circ \) Hence, we have:
\( 4x + 3x + 2x = 9x = 180^\circ \)
Solving for \( x \):
\( x = \frac{180^\circ}{9} = 20^\circ \)
The largest angle is \( 4x \):
\( 4x = 4 \times 20^\circ = 80^\circ \)
The supplementary angle of \( 80^\circ \) is:
\(180^\circ - 80^\circ = 100^\circ\)
Therefore, the correct answer is:
Final Answer: \(\boxed{100^\circ}\)
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