Triangle Angle A Calculation
In triangle ABC, the angle bisectors of angles $\angle B$ and $\angle C$ meet at point I. This point I is known as the incenter of the triangle.
There's a specific relationship between the angle at the incenter ($\angle BIC$) and the opposite angle ($\angle A$) in a triangle. The formula is:
$ \angle BIC = 90^\circ + \frac{1}{2}\angle A $
We are given that $\angle BIC = 110^\circ$. We can substitute this value into the formula to find $\angle A$.
$ 110^\circ = 90^\circ + \frac{1}{2}\angle A $
To solve for $\angle A$, first subtract $90^\circ$ from both sides:
$ 110^\circ - 90^\circ = \frac{1}{2}\angle A $
$ 20^\circ = \frac{1}{2}\angle A $
Now, multiply both sides by 2 to find the measure of $\angle A$:
$ \angle A = 2 \times 20^\circ $
$ \angle A = 40^\circ $
Therefore, the measure of angle A is $40^\circ$.
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Important Questions from Geometry
ABCDEF is a regular hexagon. Side of the hexagon is 36 cm. What is the area of the triangle AOB ?
If ∆ABC ~ ∆DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm 2, then the area of the triangle DEF is:
If Δ ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.
If ΔABC and ΔDEF are congruent triangles, then which of the following is FALSE?
D and E are points on the sides AB and AC, respectively, of ΔABC such that DE is parallel to BC and AD ∶ DB = 7 ∶ 9. If CD and BE intersect each other at F. then find the ratio of areas of ΔDEF and ΔCBF.
