Advertisements
Advertisements
Question
In ΔABC, ∠B = ∠C and ray AX bisects the exterior angle ∠DAC. If ∠DAX = 70°, then ∠ACB =
Options
35°
90°
70°
55°
Advertisements
Solution
In the given ΔABC, ∠B = ∠C . D is the ray extended from point A. AX bisects∠DAC and ∠DAX = 70°
Here, we need to find ∠ACB
As ray AX bisects ∠DAC
∠CAX = ∠DAX = 70°
Thus,
∠DAC = ∠DAX + ∠XAC
= 70° + 70°
= 140°
Now, according to the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,
∠DAC = ∠B + ∠C
140° = 2∠C
`∠C = (140°)/2`
= 70°
Thus, ∠ACB = 70°
APPEARS IN
RELATED QUESTIONS
Is the following statement true and false :
A triangle can have two right angles.
Fill in the blank to make the following statement true:
An exterior angle of a triangle is equal to the two ....... opposite angles.
In a Δ ABC, the internal bisectors of ∠B and ∠C meet at P and the external bisectors of ∠B and ∠C meet at Q, Prove that ∠BPC + ∠BQC = 180°.
In Δ ABC, if u∠B = 60°, ∠C = 80° and the bisectors of angles ∠ABC and ∠ACB meet at a point O, then find the measure of ∠BOC.
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
In the given figure, express a in terms of b.
Can a triangle together have the following angles?
55°, 55° and 80°
Find x, if the angles of a triangle is:
x°, x°, x°
Classify the following triangle according to angle:
Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Prove that ∠MOC = ∠ABC.
