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Linear Equations In Two Variables — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsLinear Equations In Two Variables5 Marks
Question
In a $\triangle\text{ABC},\ \angle\text{A}=\text{x}^\circ,$ $\angle\text{B}=(\text{3x}-2)^\circ,\ \angle\text{C}=\text{y}^\circ$ and $\angle\text{C}-\angle\text{B}=9^\circ$ Find the three angles.
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Answer

In a $\triangle\text{ABC},$
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ ...(Angle Sum Property)
⇒ x° + (3x - 2)° + y° = 180°
⇒ 4x + y = 182 ...(i)
Also, given that
$\angle\text{C}-\angle\text{B}=9^\circ$
⇒ y° - (3x - 2)° = 9°
⇒ y - 3x + 2 = 9
⇒ 3x - y = -7 ...(ii)
Adding (i) and (ii), we get
7x = 175
⇒ x = 25
Substituting x = 25 in (i), we get
⇒ y = 82
So, $\angle\text{A}=25^\circ,\ \angle\text{B}=(3\text{x} - 2)^\circ=73^\circ$ and $\angle\text{C}=82^\circ$

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