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