Advertisements
Advertisements
प्रश्न
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
पर्याय
an isosceles triangle
an obtuse triangle
an equilateral triangle
a right triangle
Advertisements
उत्तर
In the given problem, one angle of a triangle is equal to the sum of the other two angles.
Thus,
∠A = ∠B + ∠C ..........(1)
Now, according to the angle sum property of the triangle
In ΔABC
∠A + ∠B + ∠C = 180°
∠B + ∠C +∠B + ∠C = 180°
2(∠B + ∠C ) = 180°
`∠B + ∠C = (180°)/2 `
∠B + ∠C = 90° .........(2)
Further, using (2) in (1),
∠A = ∠B + ∠C
∠A = 90°
Thus, ∠A = 90°
APPEARS IN
संबंधित प्रश्न
Can a triangle have All angles equal to 60°? Justify your answer in case.
Is the following statement true and false :
An exterior angle of a triangle is less than either of its interior opposite angles.
Fill in the blank to make the following statement true:
A triangles cannot have more than ......obtuse angles.
In ΔABC, ∠B = ∠C and ray AX bisects the exterior angle ∠DAC. If ∠DAX = 70°, then ∠ACB =
An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are
The bisects of exterior angle at B and C of ΔABC meet at O. If ∠A = x°, then ∠BOC =
In the given figure, show that: ∠a = ∠b + ∠c
(i) If ∠b = 60° and ∠c = 50° ; find ∠a.
(ii) If ∠a = 100° and ∠b = 55° : find ∠c.
(iii) If ∠a = 108° and ∠c = 48° ; find ∠b.
The length of the three segments is given for constructing a triangle. Say whether a triangle with these sides can be drawn. Give the reason for your answer.
8.4 cm, 16.4 cm, 4.9 cm
S is any point on side QR of a ∆PQR. Show that: PQ + QR + RP > 2PS.
The number of triangles in the following figure is ______. Their names are ______.
