Question

В треугольниках АВС и PQR АВ=PQ, АС=РК и ВС=QR, угол Q= 50 градусов.Найдите угол В Помогите пожалуйста)) Заранее спасибо:))

Answer 1

Треугольники равно по третьему признаку равенства треугольников ⇒ Угол Q=B=50 градусов.

Answer 2

Finding the Angle B in Triangles ABC and PQR

To find the angle B in triangles ABC and PQR, we can use the given information and apply the properties of triangles.

Given: - Triangle ABC with AB = PQ, AC = RK, and BC = QR. - Angle Q = 50 degrees.

We need to find angle B.

To solve this, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Let's proceed step by step:

1. Start with triangle ABC: - AB = PQ - AC = RK - BC = QR

2. We are given that angle Q = 50 degrees.

3. Using the fact that the sum of the angles in a triangle is 180 degrees, we can find angle A in triangle ABC: - Angle A = 180 - angle B - angle C

4. Now, let's consider triangle PQR: - PQ = AB - QR = BC - PR = AC

5. Using the fact that the sum of the angles in a triangle is 180 degrees, we can find angle R in triangle PQR: - Angle R = 180 - angle P - angle Q

6. Since angle Q is given as 50 degrees, we can substitute it into the equation for angle R: - Angle R = 180 - angle P - 50

7. Now, let's compare the corresponding sides and angles of triangles ABC and PQR: - AB = PQ - AC = RK - BC = QR - Angle Q = 50 degrees

8. From the given information, we can see that triangles ABC and PQR are congruent by the Side-Angle-Side (SAS) congruence criterion.

9. Since triangles ABC and PQR are congruent, their corresponding angles are equal: - Angle A = Angle P - Angle B = Angle Q - Angle C = Angle R

10. Therefore, angle B in triangle ABC is equal to angle Q in triangle PQR, which is given as 50 degrees.

So, the angle B in triangles ABC and PQR is 50 degrees.