Chapter 4: Q8. (page 162)

Complete.
If in $△ ABC$ $m ∠ A = 50$ , $m ∠ C = 80$ , $AC = 7 x + 8$ and $BC = 38 - 3 x$ , then $x = \underline{?}$ .

Short Answer

Expert verified

The complete statement is: If in $△ A B C$ , $m ∠ A = 50$ , $m ∠ C = 80$ $A C = 7 x + 8$ and $B C = 38 - 3 x$ , then $x = 3$ .

Step by step solution

- Description of step.

It is being given that $m ∠ A = 50$ and $m ∠ C = 80$ .

As, the sum of the angles of the triangle is $180 °$ , therefore the sum of the angles $∠ A$ , $∠ B$ and $∠ C$ is $180 °$ .

Therefore, it can be obtained that:

$\begin{matrix} ∠ A + ∠ B + ∠ C = 180 \\ 50 + ∠ B + 80 = 180 \\ ∠ B + 130 = 180 \\ ∠ B = 180 - 130 \\ ∠ B = 50 \end{matrix}$

Therefore, the measure of the angle $∠ B$ is $50 °$

- Description of step.

It is being given that $A C = 7 x + 8$ and $B C = 38 - 3 x$ .

As, $m ∠ A = m ∠ B = 50$ , therefore $∠ A ≅ ∠ B$ .

As, the measures of the angles and are equal , therefore the sides opposite to the angles and are also equal.

Therefore, $A C = B C$ .

Therefore, it can be obtained that:

$\begin{matrix} A C = B C \\ 7 x + 8 = 38 - 3 x \\ 7 x + 3 x = 38 - 8 \\ 10 x = 30 \\ x = \frac{30}{10} \\ x = 3 \end{matrix}$

Therefore, the value of x is 3.

- Write the complete statement.

Therefore, the complete statement is: If in $m ∠ A = 50$ , $m ∠ C = 80$ , $A C = 7 x + 8$ and $A C = 7 x + 8$ , then x=3 .

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Complete.
If in $△ ABC$ $m ∠ A = 50$ , $m ∠ C = 80$ , $AC = 7 x + 8$ and $BC = 38 - 3 x$ , then $x = \underline{?}$ .

Short Answer

Step by step solution

- Description of step.

- Description of step.

- Write the complete statement.

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Complete.If in△ABC m∠A=50 , m∠C=80,AC=7x+8and BC=38-3x, then x=?_.

Short Answer

Step by step solution

- Description of step.

- Description of step.

- Write the complete statement.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Complete.
If in $△ ABC$ $m ∠ A = 50$ , $m ∠ C = 80$ , $AC = 7 x + 8$ and $BC = 38 - 3 x$ , then $x = \underline{?}$ .