In Δ ABC ∠B = ∠C and ray AX bisects the exterior angle ∠DAC. If – InterviewSolution

InterviewSolution

1.

In Δ ABC ∠B = ∠C and ray AX bisects the exterior angle ∠DAC. If ∠DAX =70°, then ∠ACB =A. 35°B. 90°C. 70°D. 55°

Answer»

AX bisects ∠DAC

∠CAD = 2 x ∠DAC

∠CAD = 2 x 70°

= 140°

By exterior angle theorem,

∠CAD = ∠B + ∠C

140° = ∠C + ∠C (Therefore, ∠B = ∠C)

140° = 2∠C

∠C = 70°

Therefore,

∠C = ∠ACB = 70°

Discussion

No Comment Found

Related InterviewSolutions

State whether the statements are True or False. It is possible to have a triangle in which two angles are acute.
State whether the statements are True or False. It is possible to have a triangle in which two of the angles are right angles.
State whether the statements are True or False.It is possible to have a triangle in which each angle is greater than 60°.
State whether the statements are True or False. It is possible to have a triangle in which each angle is less than 60°.
State whether the statements are True or False. It is possible to have a triangle in which each angle is equal to 60°.
In the figure y° = …………….. A) 45°B) 55°C) 90°D) 35°
In a triangle, one angle is of 90°. Then(i) The other two angles are of 45° each(ii) In remaining two angles, one angle is 90° and other is 45°(iii) Remaining two angles are complementaryIn the given option(s) which is true?(a) (i) only (b) (ii) only (c) (iii) only (d) (i) and (ii)
If two acute angles of a right triangle are equal, then each is equal toA. 30°B. 45°C. 60°D. 90°
Choose the correct one. If two angles of a triangle are 60° each, then the triangle is(a) Isosceles but not equilateral (b) Scalene(c) Equilateral (d) Right-angled
In an isosceles triangle, one angle is 70°. The other two angles are of(i) 55° and 55° (ii) 70° and 40° (iii) any measureIn the given option(s) which of the above statement(s) are true?(a) (i) only (b) (ii) only (c) (iii) only (d) (i) and(ii)