Chapter 4: Q41. (page 194)

Find the measures of $∠ ABC$ and $∠ CBD$ .

Short Answer

Expert verified

The measures of $∠ A B C$ and $∠ C B D$ are $111 °$ and $69 °$ respectively.

Step by step solution

- Observe the given diagram.

The given diagram is:

- Description of step.

From the given diagram it can be noticed that:

$m ∠ A B C = x °$ and $m ∠ C B D = (\frac{2}{3} x - 5) °$

From the given diagram it can be noticed that the angles $∠ A B C$ and $∠ C B D$ forms the linear pair.

Therefore, the sum of the angles $∠ A B C$ and $∠ C B D$ is $180 °$ .

That implies, $∠ A B C + ∠ C B D = 180$ .

Therefore, it can be obtained that:

$\begin{matrix} ∠ A B C + ∠ C B D = 180 \\ x + (\frac{2}{3} x - 5) = 180 \\ x + \frac{2}{3} x - 5 = 180 \\ x + \frac{2}{3} x = 180 + 5 \\ \frac{3 x + 2 x}{3} = 185 \\ \frac{5 x}{3} = 185 \\ x = \frac{185 \times 3}{5} \\ x = 37 \times 3 \\ x = 111 \end{matrix}$

- Find the measure of .

Substitute 111 for $x$ in $m ∠ A B C = x °$ .

Therefore, it can be obtained that:

$m ∠ A B C = 111 °$

Therefore, the measure of $∠ A B C$ is $111 °$ .

- Find the measure of .

Substitute 111 for $x$ in $m ∠ C B D = (\frac{2}{3} x - 5) °$

Therefore, it can be obtained that:

$\begin{matrix} m ∠ C B D = (\frac{2}{3} (111) - 5) ° \\ = (2 \times 37 - 5) ° \\ = (74 - 5) ° \\ = (69) ° \\ = 69 ° \end{matrix}$

Therefore, the measure of $∠ C B D$ is $69 °$ .

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Find the measures of $∠ ABC$ and $∠ CBD$ .

Short Answer

Step by step solution

- Observe the given diagram.

- Description of step.

- Find the measure of .

- Find the measure of .

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Find the measures of ∠ABC and ∠CBD.

Short Answer

Step by step solution

­- Observe the given diagram.

­- Description of step.

­- Find the measure of .

­- Find the measure of .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Find the measures of $∠ ABC$ and $∠ CBD$ .

- Observe the given diagram.

- Description of step.

- Find the measure of .

- Find the measure of .