In an isosceles triangle PQR ang P 130o If I is the in centre of the triangle then what is the value...........

Quantitative Aptitude (CPO) Geometry

In an isosceles triangle PQR, ∠P = 130^o. If I is the in-centre of the triangle, then what is the value (in degrees) of ∠QIR?

130

120

155

165

Let’s break it down:

- We’ve got triangle PQR, isosceles, with angle P = 130°.

- An isosceles triangle means two sides (and, therefore, two angles) are the same. Since P is 130°, the other two angles (Q and R) must be equal.

- Triangle angles always add up to 180°. So, Q + R = 50°, makes each Q and R = 25°.

- The incenter I sits at the intersection of the angle bisectors.

- We want ?QIR, which is the angle at the incenter between Q and R.

Here’s the thing: in any triangle, angle at incenter between points Q and R is ½ × angle at P.

So, ?QIR = ½ × 130° = 65°

Your options:

1. 130

2. 120

3. 155

4. 165

None match 65°. So, none of those are correct.

Option 3, 155°, is not correct for ?QIR. The answer is 65°, but that’s not listed. Green tick not applicable here.

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