Question

URGENT PLEASE HELP AND SHOW WORK. Solve for x.

Answer 1

6. x = 135

7. x = 23

Explanation:

Question 6

Vertical Angles Theorem: When two straight lines intersect, the opposite vertical angles are congruent.

Therefore:

`\implies \left((2)/(3)x\right)^(\circ)=(90)^(\circ)`

`\implies (2)/(3)x=90`

`\implies 3 \cdot (2)/(3)x=3 \cdot 90`

`\implies 2x=270`

`\implies (2x)/(2)=(270)/(2)`

`\implies x=135`

Question 7

Angles on a straight line sum to 180°.

Therefore:

`\implies (4x)^(\circ)+(5x-27)^(\circ)=180^(\circ)`

`\implies 4x+5x-27=180`

`\implies9x-27=180`

`\implies9x-27+27=180+27`

`\implies9x=207`

`\implies (9x)/(9)=(207)/(9)`

`\implies x=23`

Answer 2

• 6) x = 145
• 7) x = 23

Explanation:

Question 6

The marked angles are vertically opposite angles and are of equal measure per the property of vertical angles.

• (2/3)x = 90
• x = 90 : 2/3
• x = 90 *3/2
• x = 145

Question 7

The marked angles form a linear pair and their sum is a straight angle, with the measure of 180°.

• 4x + 5x - 27 = 180
• 9x - 27 = 180
• 9x = 180 + 27
• 9x = 207
• x = 207/9
• x = 23