Answer:
x = 13
Step-by-step explanation:
The sum of these two equations has to equal 180 since they are adjacent to each other. Combine the two equations with an addition sign inbetween and set it equal to 180.
5x+6+8x+5 = 180
13x+11 = 180
13x = 169
x = 169 / 13
x = 13
To check your answer plug in 13 for x in each equation, you should get 71 degrees for 5x+6 and 109 degrees for 8x+5. Adding 71 and 109 gives you 180, so the answer is correct.
∠(5x + 6)° and ∠(8x + 5)° are a linear pair, which means their sum will add upto 180° .
[tex] = 5x + 6 + 8x + 5 = 180[/tex]
[tex] = 13x + 6 + 5 = 180[/tex]
[tex] = 13x + 11 = 180[/tex]
[tex] = 13x = 180 - 11[/tex]
[tex] = 13x = 169[/tex]
[tex] = x = \frac{169}{13} [/tex]
[tex]\implies\color{olive} {\: x =\color{hotpink} 13}[/tex]
∠(5x + 6)° :-
[tex] = 5 \times 13 + 6[/tex]
[tex] = 65 + 6[/tex]
[tex]\color{olive}∠(5x + 6)°\color{hotpink} = 71° [/tex]
∠(8x + 5)° :-
[tex] = 8 \times 13 + 5[/tex]
[tex] = 104 + 5[/tex]
[tex]\color{olive}∠(8x + 5)°\color{hotpink} = 109° [/tex]
As the measure of both angles are adding up to form 180° (71+109=180), we can conclude that we have found out the correct value of x .
Therefore , the value of :-
[tex]\boxed{\color{hotpink}x = \bold13}[/tex]
