Question

If i is the incenter of triangle abc, angle abc = 65 degrees and angle acb = 55 degrees, the angle bic is, select one: a. 110 degrees b. 120 degrees c. 130 degrees d. 140 degrees

Answer 1

The correct option is b.

Step-by-step explanation:

Given information: In triangle ABC, I the incenter, ∠ABC=65° and ∠ACB=55°.

Incenter is the intersection point of all angle bisectors.

$\angle IBC=\frac{\angle ABC}{2}=\frac{65}{2}=32.5$

$\angle ICB=\frac{\angle ACB}{2}=\frac{55}{2}=27.5$

According to angle sum property the sum of all interior angles is 180° .

$\angle IBC+\angle ICB+\angle BIC=180^{\circ}$

$32.5+27.5+\angle BIC=180$

$60+\angle BIC=180$

$\angle BIC=180-60$

$\angle BIC=120$

The measure of angle BIC is 120 °.

Therefore, the correct option is b.

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