Question

Need help with this, thanks

Answer 1

The error is that vertical angles are congruent, and don't necessarily add to 180°. Vertical angles only add to 180° if they are right angles.

`13x+45+19x+3=180 \\ \\ 32x+48=180 \\ \\ 32x=132 \\ \\ x=33/8`

Answer 2

x = 7

Explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent.

Angles on a Straight Line Theorem

The sum of angles formed on a straight line is equal to 180°.

The error made is confusing the Vertical Angle Theorem with the Angles on a Straight Line Theorem. To find x, we should either:

• Equal a pair of vertical angles and solve for x, or
• Equal the sum a pair of angles that form a straight line to 180° and solve for x.

Applying the Vertical Angle Theorem:

`\boxed{\begin{aligned} (13x+45)^(\circ) &=(19x+3)^(\circ) \\13x+45&=19x+3\\13x+42&=19x\\42&=6x\\x&=7\end{aligned}}`

Applying the Angles on a Straight Line Theorem:

`\boxed{\begin{aligned}(6x+2)^(\circ)+(19x+3)^(\circ)&=180^(\circ)\\6x+2+19x+3&=180\\25x+5&=180\\25x&=175\\x&=7\end{aligned}}`

Therefore, the value of x is
`\boxed{x=7}` .