Question

This prob easy for yall but ion have a way of learning it

Answer 1

`\textsf{12)} \quad x=\boxed{12}`

`\textsf{13)} \quad x=\boxed{43}`

Explanation:

Question 12

According to the Vertical Angle Theorem, when two lines intersect, the pairs of opposite (or vertical) angles formed are congruent, meaning they have equal measures. In other words, if two lines intersect at a point, the angles that are opposite to each other are of equal size.

The given diagram shows two intersecting lines with one pair of opposite angles labeled. Therefore, to find the value of x, equate the given angles and solve for x.

`\begin{aligned}(5x-48)^(\circ)&=x^(\circ)\\5x-48&=x\\5x-48-x&=x-x\\4x-48&=0\\4x-48+48&=0+48\\4x&=48\\4x/4&=48/4\\x&=12\end{aligned}`

Therefore, the value of x is 12.

`\hrulefill`

Question 13

A linear pair refers to a pair of adjacent angles that are formed when two lines intersect. As these angles form a straight line, the sum of the measures of the two angles in a linear pair is always equal to 180°.

The given diagram shows two intersecting lines with one pair of adjacent angles labeled. Therefore, to find the value of x, set the sum of the adjacent angles to 180°, and solve for x.

`\begin{aligned}(3x+8)^(\circ)+x^(\circ)&=180^(\circ)\\3x+8+x&=180\\4x+8&=180\\4x+8-8&=180-8\\4x&=172\\4x/4&=172/4\\x&=43\end{aligned}`

Therefore, the value of x is 43.

Answer 2

`\textsf{For 1st one: } \sf x = \boxed{ 12^\circ}`

`\textsf{For 2nd one: } \sf x = \boxed{ 43^\circ}`

Explanation:

For 1st Question:

Pair of given angles in the picture is vertically opposite angles.

Since,

Vertically opposite angles are two or more angles that are opposite each other at a vertex and are created by two straight intersecting lines.

Vertically opposite angles are equal to each other.

So,

we can write it as:

`\sf x^\circ = (5x-48)^\circ`

Since both angles have the same measure, the expressions inside the parentheses must be equal.

Therefore:

`\sf x = 5x - 48`

Subtract 5x from both sides:

`\sf x - 5x = -48`

Simplify like terms:

`\sf -4x = -48`

Divide by -4 to isolate x:

`\sf (-4x)/(-4) =(-48)/(-4)`

Simplify:

`\sf x = 12`

So, value of x is 12°.

`\sf \hrulefill`

For the 2nd Question:

Pair of given angles in the picture is linear pair or angle in a straight line.

Since

A linear pair is a pair of adjacent angles formed by two intersecting lines.

The linear pair of angles are always supplementary as they form on a straight line.

In other words, the sum of two angles in a linear pair is always 180°.

So,

We can write it as:

`\sf x^\circ+ (3x+8)^\circ =180^\circ`

Let's isolate the value of x.

Open Parentheses or bracket:

`\sf x+3x+8 =180`

Simplify like terms:

`\sf 4x +8 =180`

Subtract 8 both sides:

`\sf 4x +8-8 =180-8`

`\sf 4x =172`

Divide by 4 on both sides:

`\sf ( 4x)/(4) =(172)/(4)`

Simplify:

`\sf x = 43`

Therefore, value of x is 43°.