Question

В трикутнику СКЕ проведена медіана СА причому СА=АЕ кут Е=69 градусів. Знайти кут КАС

Answer 1

Т.к. треугольник АСЕ равнобедренный (потому что СА=АЕ),то угол АСЕ=АЕС=69,то угол АСЕ=180-(69+69)=42
т.к. углы КАС и САЕ смешные следовательно САК=180-42=138
Ответ:138

Answer 2

Problem Analysis

We are given a triangle SKЕ with a median SA, where SA = AE and angle E = 69 degrees. We need to find angle KAS.

Solution

To find angle KAS, we can use the fact that the medians of a triangle divide each other in a 2:1 ratio. This means that the length of AS is twice the length of SK.

Let's assume that SK = x. Since AS is twice the length of SK, we have AS = 2x.

Since SA = AE, we have AE = 2x as well.

Now, let's consider triangle SAE. We know that the sum of the angles in a triangle is 180 degrees. We can use this information to find angle SAE.

Let angle SAE be y. Then, angle SEA is also y because SA = AE.

We also know that angle E = 69 degrees.

Using the fact that the sum of the angles in a triangle is 180 degrees, we can write the equation:

y + y + 69 = 180

Simplifying the equation, we get:

2y + 69 = 180

Subtracting 69 from both sides, we have:

2y = 111

Dividing both sides by 2, we get:

y = 55.5

Now, we can find angle KAS by subtracting angle SAE from angle EAS.

Angle KAS = angle EAS - angle SAE

Angle KAS = 69 - 55.5

Angle KAS = 13.5 degrees

Therefore, the measure of angle KAS is 13.5 degrees.

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