Question

Find all possible values of x for which these two triangles are similar. 1 x + 10° 2x - 50° o TAT The only possible values of x are 4 and

Answer 1

we know that

If two triangles are similar, then their corresponding angles are congruent

In this problem

we have that

First case

angle x and angle 60 are corresponding angles

angle (x+10) and angle (2x-50) are corresponding angles

so

x=60

x+10=2x-50

2x-x=10+50

x=60

is ok

Second case

angle (x+10) and angle 60 are corresponding angles

angle x and angle (2x-50) are corresponding angles

so

x+10=60

x=50

x=2x-50

2x-x=50

x=50

therefore

the possibles values of x are 50 degrees and 60 degrees