Question

In the given figure, AB=AD. ∠ACB=95°+ ∠BAC and ∠BAD=150°. Find ∠ACB.

• A. 100°
• B. 110°
• C. 120°
• D. 130°

Answer 1

The Correct Option is D

To find ∠ACB, we use the given information and properties of a triangle.

We know that triangle ABC has AB = AD, which means triangle ABD is isosceles, hence ∠ABD = ∠BAD = 150°.

Let's denote the required angle ∠ACB as x.

We have the equation for the triangle rule:

∠ACB = 95° + ∠BAC

Since triangle ABC's total angle is 180°, we write:

∠ACB + ∠ABC + ∠BAC = 180°

Given that ∠BAD = 150°, triangle ABD being isosceles implies @@∠ABD = ∠ADB = (180° - 150°) / 2 = 15°@@. But, since ∠ABD and ∠BAC are distinct as they belong to different angles in overlapping triangles, we focus on the correct adjustment of angles in triangle ABC:

∠ABC = 15°

Substitute back into the triangle angle sum equation:

x + 15° + z = 180°

Also given:

x = 95° + z

Substituting z from the first equation in the second:

95° + z + 15° + z = 180°

Simplifying,

110° + 2z = 180°

Subtract 110° both sides:

2z = 70°

Then,

z = 35°

This implies:

x = 95° + 35° = 130°

Thus, ∠ACB equals 130°.

Options	Correct Answer
100°	110°
120°	130°