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

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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.

User Mattias Nordqvist
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