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Summary

In this video, the concept of complementary angles is explored using a geometry problem. The example involves two angles, angle ABD and angle DBC, which together form a right angle (90°). The angles are expressed in terms of a variable 'y', where angle ABD is 11y° and angle DBC is 7y°. By setting the sum of the two angles equal to 90° and solving for 'y', the value is found to be 5°. The final step calculates angle DBC, which is 35°. The video provides a clear, step-by-step explanation of how to solve the problem.

Takeaways

• 😀 The video explains complementary and right-angle angles.
• 😀 The problem in the video involves two angles: angle ABD = 11y° and angle DBC = 7y°.
• 😀 The task is to find the value of 'y' and the measure of the right angle ABD.
• 😀 The sum of angles ABD and DBC forms a right angle, meaning they add up to 90°.
• 😀 The sum of the two angles is expressed as 18y° = 90°.
• 😀 To find 'y', we divide 90° by 18, yielding y = 5°.
• 😀 With y determined as 5°, the measure of angle DBC can now be calculated as 7y = 35°.
• 😀 The measure of angle ABD is 11y°, which becomes 55° when y = 5°.
• 😀 The right angle ABC is made up of angles ABD and DBC.
• 😀 The solution emphasizes using basic angle relationships to solve the problem.

Q & A

What is the main topic discussed in the video?

The main topic discussed is complementary and right angle angles, specifically in the context of solving for unknown angles in geometric problems.

What is the relationship between angle ABD and angle DBC in the problem?

Angle ABD and angle DBC are complementary, meaning they add up to 90° because they form a right angle together.

How can we solve for the unknown value 'y' in the problem?

We solve for 'y' by setting up an equation: the sum of angle ABD (11y) and angle DBC (7y) equals 90°. Thus, 11y + 7y = 90°, which simplifies to 18y = 90°. Solving for 'y', we get y = 90° / 18 = 5°.

What does the angle ABD represent in the problem?

Angle ABD represents one of the angles in the right triangle, and it is given as 11y° in the problem.

How is the size of angle DBC determined?

The size of angle DBC is determined by substituting the value of y (5°) into the expression for angle DBC, which is 7y°. Therefore, 7 * 5° = 35°.

Why does the sum of the two angles equal 90°?

The sum of the two angles equals 90° because angle ABD and angle DBC together form a right angle, and the sum of the angles in a right angle is always 90°.

What is the value of 'y' after solving the equation?

After solving the equation 18y = 90°, the value of 'y' is 5°.

What does the value of 35° represent in the problem?

The value of 35° represents the measure of angle DBC after substituting y = 5° into the expression for angle DBC.

What is the significance of angle EBC in the problem?

Angle EBC is significant because it is the complementary angle to angle ABC, forming a right angle together with angle ABD.

How does this video help in understanding complementary angles?

The video explains how complementary angles work by showing how to solve for unknown angles using algebra, helping to understand the relationship between angles that add up to 90°.