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Lines and Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
MCQ
An exterior angle of a triangle is $110^\circ $ and its two interior opposite angles are equal. Each of these equal angles is:
  • A
    $70^\circ$
  • B
    $35^\circ$
  • ✓
    $55^\circ$
  • D
    $27\frac{1}{2}^\circ$
✓

Answer

Correct option: C.
$55^\circ$
Let the measure of each of the two equal interior opposite angles of the triangle be $x.$
In a triangle, the exterior angle is equal to the sum of the two interior opposite angles.
$\therefore$ $x + x = 110^\circ$
$\Rightarrow 2x = 110^\circ$
$\Rightarrow x = 55^\circ$
Thus, the measure of each of these equal angles is $55^\circ .$

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