Can someone help me please?

Question

asked Jun 11, 2023 54.5k views

2 Answers

Adam Spicer · Answer 1 · 2023-06-11T19:36:01+0000

(8x+9)° is co-interior with an angle vertical opposite with 99°

That makes it:

(8x+9)°+99°=180°(co-interior angles are supplementary)

$8x+108=180\\8x=180-108\\8x=72\\(8x)/(8) =(72)/(8) \\x=9$

Questionable · Answer 2 · 2023-06-17T19:30:02+0000

Answer:

$x=\boxed{9}$

$\textsf{Step 1}: \quad (8x + 9)^(\circ) + 99^(\circ) = \boxed{180}\;^(\circ)$

$\textsf{Step 2}: \quad 8x + \boxed{108} = \boxed{180}$

$\textsf{Step 3}: \quad 8x=\boxed{72}$

$\textsf{Step 4}: \quad x=\boxed{9}$

Explanation:

Alternative Exterior Angles Theorem

When a straight line intersects two parallel straight lines, the resulting alternate exterior angles are congruent.

Applying the Alternative Exterior Angles Theorem:

$\implies \angle 3 = 99^(\circ)$

Step 1

Angles on a straight line sum to 180°.

$\implies (8x + 9)^(\circ) + \angle 3 = 180^(\circ)$

$\implies (8x + 9)^(\circ) + 99^(\circ) = \boxed{180}\;^(\circ)$

Step 2

Add the constants:

$\implies 8x+9+99=180$

$\implies 8x + \boxed{108} = \boxed{180}$

Step 3

Subtract 108 from both sides:

$\implies 8x+108-108=180-108$

$\implies 8x=\boxed{72}$

Step 4

Divide both sides by 8:

$\implies 8x / 8 = 72 / 8$

$\implies x=\boxed{9}$