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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
In a $\triangle ABC , \angle A =x^{\circ}, \angle B =(3 x-2)^{\circ}, \angle C =y^{\circ}$. Also $\angle C -\angle B =9^{\circ}$. The sum of the greatest and the smallest angles of this triangle is
  • ✓
    $107^{\circ}$
  • B
    $135^{\circ}$
  • C
    $155^{\circ}$
  • D
    $145^{\circ}$
✓

Answer

Correct option: A.
$107^{\circ}$
$\angle A = x ^{\circ}, \angle B =3 x -2^{\circ}$ and $\angle C = y ^{\circ}$
Sum of angles in a triangle is $180^{\circ}$
Therefore, $x+3 x-2+y=180^{\circ}$
or $4 x + y =182 \ldots \ldots(i)$
Also, $\angle C -\angle B =90^{\circ}$
or $ y-(3 x-2)=90^{\circ}$
or $ y-3 x=70^{\circ} \ldots \ldots(ii)$
Subtracting $(ii)$ from $(i),$ we get
$7 x=175$
or $ x=250$
Put $x=25^{\circ}$ in $(ii),$ we get $y=82^{\circ}$
Therefore,
$\angle A=25^{\circ}, \angle B=3 x-2$
$=3(25)-2=73^{\circ}$
And $\angle C = y ^{\circ}$
Sum of greatest and smallest angle
$=82^{\circ}+25^{\circ}=107^{\circ}$

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