Answer:
x = 25
scalene, acute
Step-by-step explanation:
Sum of the interior angles of a triangle = 180°
[tex]\implies (2x+11)+(3x-7)+(2x+1)=180[/tex]
[tex]\implies 2x+11+3x-7+2x+1=180[/tex]
Collect like terms:
[tex]\implies 2x+3x+2x+1+11-7=180[/tex]
Combine like terms:
[tex]\implies 7x+5=180[/tex]
Subtract 5 from both sides:
[tex]\implies 7x=175[/tex]
Divide both sides by 7:
[tex]\implies x=25[/tex]
Substituting found value of [tex]x[/tex] into the three angle expressions:
∠A = (2 x 25) + 11 = 61°
∠B = (3 x 25) - 7 = 68°
∠C = (2 x 25) + 1 = 51°
This is a scalene triangle as it has three different angles and three different side lengths (non-congruent).
It is also an acute triangle as all interior angles are less than 90°
