Advertisements
Advertisements
प्रश्न
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
पर्याय
100°
120°
110°
130°
Advertisements
उत्तर
Let ABCbe isosceles triangle
Then
AB = AC
∠B = ∠C
Now it is given that vertex angle is 2 times the sum of base angles
⇒∠A = 2 ∠(B+ C)
⇒∠A = 2 ∠(∠B + ∠B ) (As ∠B = ∠C)
⇒∠A = 2 (2∠B)
⇒∠A = 4 ∠B
Now
∠A + ∠B + ∠C = 180° (Property of triangle)
4∠B + ∠B + ∠B = 180° (Since ∠A = 4∠B, and ∠B = ∠C )
6∠B = 180°
∠B = 30°
∠A = 4∠B
`= 4 xx 30°`
= 120°
APPEARS IN
संबंधित प्रश्न
In a squared sheet, draw two triangles of equal areas such that
The triangles are congruent.
What can you say about their perimeters?
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
Prove that the sum of three altitudes of a triangle is less than the sum of its sides.
ΔPQR and ΔABC is not congruent to ΔRPQ, then which of the following is not true:
In the given figure, the measure of ∠B'A'C' is
From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.
The following figure 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: ΔAMC≅ ΔANB
State, whether the pairs of triangles given in the following figures are congruent or not:
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent angles
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side AB of ∆ABC so that the two triangles are congruent? Give reason for your answer.
