Angle A of triangle ABC is 360. ∠BCD is the outer angle of triangle ABC and is equal to 1170. Find angle B.

Angle A of triangle ABC is 360. ∠BCD is the outer angle of triangle ABC and is equal to 1170. Find angle B. Side BC is 2 times less than side AB and side AC is 2 cm larger than BC. Find the sides of the triangle if its perimeter is 18 cm.

Decision.
one). To find the angle B of the triangle ABC, we will use the property of the external angle of the triangle, from which it follows that the sum of the internal angles that are not adjacent to it is equal to the value of this external angle, that is, +BAC + ∠CBA = ∠BCD. Let ∠СВА = Х. Since it is known from the condition of the problem that the angle A of the triangle ABC is equal to 36 °, and ∠BCD is the outer angle of the triangle ABC and is equal to 117 °, then substituting the values ​​of the angles into the equality, we can compose the equation:
36 ° + X = 117 °;
X = 117 ° – 36 °;
X = 81 ° – величинаСВА value.
Answer: The ∠CBA value is 81 °.
2). Let the length of the BC side be x cm, then the AB length will be (2 ∙ x) cm, since it is known from the problem statement that the BC side is 2 times less than the AB side. Then the length of the AC side will be (x + 2) cm, since the AC side is 2 cm larger than the BC. Knowing that the perimeter of the triangle is 18 cm, we make the equation:
x + 2 ∙ x + (x + 2) = 18;
4 ∙ x = 18 – 2;
x = 16: 4;
x = 4 (cm) – BC side length;
2 ∙ 4 = 8 (cm) – side length AB;
4 + 2 = 6 (cm) – side length of the speaker.
Answer: the sides of the triangle are 4 cm, 6 cm and 8 cm.