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Chapter 4: Q. 355 (page 480)

The measure of one of the small angles of a right triangle is 15less than twice the measure of

the other small angle. Find the measure of both angles.

Short Answer

Expert verified

The measures of the angles are55and35

Step by step solution

01

Step 1. Given information

The measure of one of the small angles of a right triangle is 15less than twice the measure of

the other small angle.

02

Step 2. Find the angles

Let angles to be xand y

x+y=90

Now using the given condition,

x=2y-15

Put this value of xin other equation,

x+y=902y-15+y=903y=105y=35

Now put this value of yin any of the equation,

x+y=90x+35=90x=55

The measures of the angles are 35 and55

03

Step 3. Check by substituting values in both the equations

Substitute x=55,y=35in both the equations

x+y=9055+35=9090=90

This is true

x=2y-1555=2(35)-1555=70-1555=55

This is also true

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