Given:
Two angles are Complementary.
One angle measures (2x-16) degrees.
The other measures (x +1) degrees.
To find:
The value of the larger angle.
Solution:
Let,
[tex]\angle 1=(2x-16)^\circ[/tex]
[tex]\angle 2=(x+1)^\circ[/tex]
We know that, sum of two complementary angles is 90 degrees. Since, given angles are complementary angles, therefore
[tex]\angle 1+\angle 2=90^\circ[/tex]
[tex](2x-16)^\circ+(x+1)^\circ=90^\circ[/tex]
[tex](3x-15)^\circ=90^\circ[/tex]
Now,
[tex]3x-15=90[/tex]
[tex]3x=90+15[/tex]
[tex]3x=105[/tex]
Divide both sides by 3.
[tex]x=35[/tex]
The value of x is 35.
[tex]\angle 1=(2(35)-16)^\circ[/tex]
[tex]\angle 1=(70-16)^\circ[/tex]
[tex]\angle 1=(54)^\circ[/tex]
And,
[tex]\angle 2=(35+1)^\circ[/tex]
[tex]\angle 2=(36)^\circ[/tex]
Therefore, the value of the larger angle is 54 degrees.
