We know that : The Sum of the angles in a triangle should be equal to 180°
Given : The Triangle is a Right angled Triangle
It means : One of the Angle in the triangle is 90°
It means : The sum of the other two angles should be equal to 90°
Given : One acute angle is 8x + 5 and the other one is 4x + 9
⇒ 8x + 5 + 4x + 9 = 90°
⇒ 12x + 14 = 90°
⇒ 12x = 76°
⇒ x = 6.333°
The larger angle among the acute angles is 8x + 5
⇒ 8(6.333) + 5
⇒ 50.67 + 5
⇒ 55.67
[tex]\huge\bold{Given :}[/tex]
Angle 1 = ( 8x + 5 ) ...(i)
Angle 2 = ( 4x + 9 ) ...(ii)
Angle 3 = 90° ( ∵ it is a right-angled triangle )
[tex]\huge\bold{To\:find :}[/tex]
The value of the larger angle of the two acute angles.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]{\boxed{\mathcal{\red{ A. \:55.67° .\:}}}}[/tex]. ✅
[tex]\large\mathfrak{{\pmb{\underline{\blue{Step-by-step\:explanation}}{\blue{:}}}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ ∠ 1 + ∠ 2 + ∠ 3 = 180°
➪ 8x + 5 + 4x + 9 + 90° = 180°
➪ 12x + 104° = 180°
➪ 12x = 180° - 104°
➪ 12x = 76°
➪ x = [tex] \frac{76° }{12} [/tex]
➪ x = 6.333°
The value of x is 6.333°.
Now,
Substituting the value of x in eq. (i) & (ii), we have
Angle 1 = 8x + 5
= 8 x 6.333 + 5
= 50.666 + 5
= 55.67°
Angle 2 = 4x + 9
= 4 x 6.333 + 9
= 25.332 + 9
= 34.332°
Clearly, angle 1 is greater than angle 2.
Therefore, the value of the larger angle of the two acute angles is 55.67°.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
