Question

In a right triangle one angle measure 28° more than the other acute angle. Use equations to solve for the measures of the two unknown angles.

Answer 1

One acute angle is 31 degrees and the other acute angle is ( 31+28=) 59 degrees.

Explanation:

In the right angled triangle one angle is always equal to 90 degrees.

Suppose <a= 90 degrees

< b= x degrees

< c= x+28 degrees

The sum of all the angles of the triangle are always equal to 180 degrees

therefore

<a+ <b+<c= 90 + x+ x+28 = 180

or

2x= 180- 28- 90

2x=62

x= 31 degrees

One acute angle is 31 degrees and the other acute angle is ( 31+28=) 59 degrees.

An acute angle is an angle which has less than 90 degrees in measurement .

Hence both angles of the right angle triangle are acute angles , 31 and 59 degrees.