Question

URGENT PLEASE HELP AND SHOW WORK. Solve for x.

Answer 1

Answer:

6.  x = 135

7.  x = 23

Step-by-step explanation:

Question 6

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

Therefore:

$\implies \left(\dfrac{2}{3}x\right)^{\circ}=(90)^{\circ}$

$\implies \dfrac{2}{3}x=90$

$\implies 3 \cdot \dfrac{2}{3}x=3 \cdot 90$

$\implies 2x=270$

$\implies \dfrac{2x}{2}=\dfrac{270}{2}$

$\implies x=135$

Question 7

Angles on a straight line sum to 180°.

Therefore:

$\implies (4x)^{\circ}+(5x-27)^{\circ}=180^{\circ}$

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

$\implies9x-27=180$

$\implies9x-27+27=180+27$

$\implies9x=207$

$\implies \dfrac{9x}{9}=\dfrac{207}{9}$

$\implies x=23$

Answer 2

Answer:

• 6) x = 145
• 7) x = 23

Step-by-step 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