Advertisements
Advertisements
प्रश्न
In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that ADbisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is
विकल्प
72°
73°
74°
95°
उत्तर
It is given that
∠B = 2∠C,
AB = CD
∠BAD = DAC
∠ABE = ∠EBC
We have to find ∠BAC
Now AB = CD
AB = BD
Now the triangle is isosceles
∠B = 2∠C
Let
∠B = x
∠B = 2x
∠C = x
So ∠B = ∠A
Now
∠A + ∠B + ∠C = 180°
2x + 2x + x = 180°
5x = 180°
x = 36°
Since
∠A = 2x
= `2 xx 36°
= 72°
APPEARS IN
संबंधित प्रश्न
In the given figure, if AB = AC and ∠B = ∠C. Prove that BQ = CP.
In ΔPQR ≅ ΔEFD then ED =
In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: (i) AM = AN (ii) ΔAMC ≅ ΔANB
In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that: AD = CE.
In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent angles
If AB = QR, BC = PR and CA = PQ, then ______.
In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if ______.
