Chapter 1: Q11. (page 53)

In the triangle below, $x$ and $y$ are integers. If $25 < y < 30$ , what is one possible value of $x$ ?

Short Answer

Expert verified

The one possible value of x is128.

Step by step solution

- Label the given diagram.

The labelled diagram is:

- Description of step.

The sum of the angles of a triangle is $180 °$ .

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

Therefore, it can be obtained that:

$\begin{matrix} ∠ B A C + ∠ A B C + ∠ A C B = 180 ° \\ y ° + x ° + y ° = 180 ° \\ (x + 2 y) ° = 180 ° \\ \Rightarrow x + 2 y = 180 \end{matrix}$

- Description of step.

It is given that $25 < y < 30$ and y is an integer.

Therefore, one of the possible value of y is 26.

Now, find the value of x by substituting 26 for y into $x + 2 y = 180$ .

Therefore, it can be obtained that:

$\begin{matrix} x + 2 y = 180 \\ x + 2 (26) = 180 \\ x + 52 = 180 \\ x = 180 - 52 \\ x = 128 \end{matrix}$

Therefore, the value of x is 128.

- Description of step.

Therefore, one of the possible value of x is 128.

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In the triangle below, $x$ and $y$ are integers. If $25 < y < 30$ , what is one possible value of $x$ ?

Short Answer

Step by step solution

- Label the given diagram.

- Description of step.

- Description of step.

- Description of step.

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In the triangle below, xand yare integers. If 25<y<30, what is one possible value of x?

Short Answer

Step by step solution

­- Label the given diagram.

­- Description of step.

­- Description of step.

­- Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Decision Maths

Calculus

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In the triangle below, $x$ and $y$ are integers. If $25 < y < 30$ , what is one possible value of $x$ ?

- Label the given diagram.

- Description of step.

- Description of step.

- Description of step.