Question

треугольник АВС и МКЕ подобны,причем АВ:КМ=ВС:ЕК=АС:ЕМ,угол А=40,Е=56градусов.Чему равен угол В?

Answer 1

Т.к. треугольники подобны=> углы равны=>
180-(40+56)=84

Answer 2

E = C
B = 180 - (A + C) = 84°

Answer 3

Understanding the Problem

The problem states that triangles ABC and MKE are similar, and the ratios of their corresponding sides are equal. Additionally, it mentions that angle A is 40 degrees and angle E is 56 degrees. The question asks for the measure of angle B.

Solution

To solve for the measure of angle B, we can use the properties of similar triangles and the given angle measures.

Given: Triangle ABC is similar to triangle MKE AB:KM = BC:KE = AC:ME Angle A = 40 degrees Angle E = 56 degrees

Using the Properties of Similar Triangles

1. We know that in similar triangles, the corresponding angles are equal. 2. We also know that the ratio of the corresponding sides of similar triangles is equal.

Applying the Angle and Side Ratios

We can use the given angle measures and side ratios to determine the measure of angle B.

Step 1: Finding the Ratio of Angle Measures

Since triangles ABC and MKE are similar, the measure of angle B in triangle ABC will be equal to the measure of the corresponding angle in triangle MKE. Let's call this angle x.

Step 2: Using the Angle Measures

We can use the given angle measures to find the measure of angle x. We know that: Angle A = 40 degrees Angle E = 56 degrees

Since angle A and angle E are corresponding angles in the similar triangles, we can set up the following equation: 40 / x = 56 / 56

Solving for x: 40 / x = 56 / 56 40 / x = 1 x = 40

So, the measure of angle B, denoted by x, is 40 degrees.

Conclusion

The measure of angle B in triangle ABC is 40 degrees.

If you have any further questions or need additional assistance, feel free to ask!