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Chapter 4: Q41. (page 194)

Find the measures of $鈭� ABC$ and $鈭� CBD$ .

Short Answer

Expert verified

The measures of $鈭� A B C$ and $鈭� C B D$ are $111 掳$ and $69 掳$ respectively.

Step by step solution

01

- Observe the given diagram.

The given diagram is:

02

- Description of step.

From the given diagram it can be noticed that:

$m 鈭� A B C = x 掳$ and $m 鈭� C B D = (\frac{2}{3} x - 5) 掳$

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

Therefore, the sum of the angles $鈭� A B C$ and $鈭� C B D$ is $180 掳$ .

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

Therefore, it can be obtained that:

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

03

- Find the measure of .

Substitute 111 for $x$ in $m 鈭� A B C = x 掳$ .

Therefore, it can be obtained that:

$m 鈭� A B C = 111 掳$

Therefore, the measure of $鈭� A B C$ is $111 掳$ .

04

- Find the measure of .

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

Therefore, it can be obtained that:

$\begin{matrix} m 鈭� C B D = (\frac{2}{3} (111) 鈭� 5) 掳 \\ = (2 脳 37 鈭� 5) 掳 \\ = (74 鈭� 5) 掳 \\ = (69) 掳 \\ = 69 掳 \end{matrix}$

Therefore, the measure of $鈭� C B D$ is $69 掳$ .

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