38. In a right triangle, if one acute angle has measure 8x + 5 and the other has measure 4x + 9, find the larger of these two angles.
55.67
62.4
57.92
64.61
None of the above

Angle 1 = ( 8x + 5 ) ...(i)

Angle 2 = ( 4x + 9 ) ...(ii)

Angle 3 = 90° ( ∵ it is a right-angled triangle )

The value of the larger angle of the two acute angles.

. ✅

We know that,

➪ ∠ 1 + ∠ 2 + ∠ 3 = 180°

➪ 8x + 5 + 4x + 9 + 90° = 180°

➪ 12x + 104° = 180°

➪ 12x = 180° - 104°

➪ 12x = 76°

➪ x =

➪ 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°.