Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![### Geometry Problem: Find the Value of \( x \)
**Problem Statement:**
15. Find the value of \( x \).
**Diagram Explanation:**
The provided diagram shows two intersecting lines and a transversal. The angles formed at the intersection are labeled as follows:
- One angle is labeled \( 128^\circ \).
- The vertically opposite angle to this is labeled \( 2x^\circ \).
**Step-by-Step Solution:**
1. Recognize that vertically opposite angles are equal. Therefore:
\[
2x^\circ = 128^\circ
\]
2. Solve for \( x \):
\[
x = \frac{128^\circ}{2} = 64^\circ
\]
**Conclusion:**
The value of \( x \) is \( 64^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0806c0e-0103-48e4-89cd-443bacc85606%2F4376132d-80e8-41a1-8d1b-06b885aef6fa%2F8t45mmc_processed.jpeg&w=3840&q=75)
![**Problem 14.**
Given a triangle with the following properties:
- One of the angles is 43°.
- The triangle is isosceles, as indicated by the two equal sides marked with a hash line.
- The angles opposite the equal sides are marked \( x \) and \( y \), respectively.
We need to find the values of \( x \) and \( y \).
**Analysis:**
In an isosceles triangle, the angles opposite the equal sides are equal. Hence, \( x = y \).
Additionally, the sum of all internal angles in a triangle is always \( 180^\circ \).
**Calculation:**
Let us denote the three angles of the triangle as \( 43^\circ \), \( x \), and \( y \). As established, \( x = y \).
Thus:
\[ x + y + 43^\circ = 180^\circ \]
Since \( x = y \), we replace \( y \) with \( x \), giving:
\[ x + x + 43^\circ = 180^\circ \]
\[ 2x + 43^\circ = 180^\circ \]
Subtracting \( 43^\circ \) from both sides, we get:
\[ 2x = 137^\circ \]
Dividing both sides by 2:
\[ x = 68.5^\circ \]
Since \( x = y \):
\[ y = 68.5^\circ \]
Therefore:
\[ x = 68.5 \]
\[ y = 68.5 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0806c0e-0103-48e4-89cd-443bacc85606%2F4376132d-80e8-41a1-8d1b-06b885aef6fa%2F8sua7dc_processed.jpeg&w=3840&q=75)
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