Question

У прямокутному трикутнику ABC з прямим кутом A проведена бісектриса BD. Знайти кут трикутника ABD, якщо культури ADB = 75°

Answer 1

Finding the Angle ABD in a Right Triangle

To find the angle ABD in a right triangle ABC with a right angle at A and the bisector BD, we can use the properties of angles in a triangle.

Let's break down the problem step by step:

1. We are given that triangle ABC is a right triangle with a right angle at A and that angle ADB is 75°. 2. Since angle ADB is a bisector, it divides angle ABC into two equal angles, ABD and DBC. 3. We need to find the measure of angle ABD.

To find angle ABD, we can use the fact that the sum of the angles in a triangle is 180°. Since triangle ABC is a right triangle, we know that angle ABC is 90°. Therefore, we can write the equation:

angle ABD + angle DBC + angle ABC = 180°

Since angle ABC is 90°, we can substitute its value into the equation:

angle ABD + angle DBC + 90° = 180°

Simplifying the equation, we get:

angle ABD + angle DBC = 90°

Since angle ADB is 75°, we can substitute its value into the equation:

75° + angle DBC = 90°

Now, we can solve for angle DBC:

angle DBC = 90° - 75° angle DBC = 15°

Therefore, the measure of angle DBC is 15°.

To find the measure of angle ABD, we can substitute the value of angle DBC into the equation:

angle ABD + 15° = 90°

Simplifying the equation, we get:

angle ABD = 90° - 15° angle ABD = 75°

Therefore, the measure of angle ABD is 75°.

In summary, in the given right triangle ABC with a bisector BD and angle ADB measuring 75°, the measure of angle ABD is also 75°.

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