Advertisements
Advertisements
प्रश्न
In ΔABC, ∠B = ∠C and ray AX bisects the exterior angle ∠DAC. If ∠DAX = 70°, then ∠ACB =
पर्याय
35°
90°
70°
55°
Advertisements
उत्तर
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
संबंधित प्रश्न
In a ΔABC, ∠ABC = ∠ACB and the bisectors of ∠ABC and ∠ACB intersect at O such that ∠BOC = 120°. Show that ∠A = ∠B = ∠C = 60°.
In Fig. 10.25, AB = AC and DB = DC, find the ratio ∠ABD : ∠ACD.
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 always ......... than either of the interior opposite angles.
In ΔPQR, If ∠R > ∠Q then ______.
Find the unknown marked angles in the given figure:
The angle of a vertex of an isosceles triangle is 100°. Find its base angles.
Can a triangle together have the following angles?
85°, 95° and 22°
Classify the following triangle according to angle:
In the following figure, AD is the bisector of ∠BAC. Prove that AB > BD.
