Question

Two angles areComplementary One angle measures (2x-16) degrees. The other measures (x +1) degrees. What is the value of the larger angle?

Answer 1

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,

$\angle 1=(2x-16)^\circ$

$\angle 2=(x+1)^\circ$

We know that, sum of two complementary angles is 90 degrees. Since, given angles are complementary angles, therefore

$\angle 1+\angle 2=90^\circ$

$(2x-16)^\circ+(x+1)^\circ=90^\circ$

$(3x-15)^\circ=90^\circ$

Now,

$3x-15=90$

$3x=90+15$

$3x=105$

Divide both sides by 3.

$x=35$

The value of x is 35.

$\angle 1=(2(35)-16)^\circ$

$\angle 1=(70-16)^\circ$

$\angle 1=(54)^\circ$

And,

$\angle 2=(35+1)^\circ$

$\angle 2=(36)^\circ$

Therefore, the value of the larger angle is 54 degrees.