Question

Could someone please help me solve this question? Thanks! (Click image to see question)

Answer 1

We will have the following:

*First: From properties of the rhombus the following is true:

$m<1=m<6\Rightarrow m<1=65$$m<2=m<6\Rightarrow m<2=65$

*Second: We know that the sum of all internal angles of a quadrilateral add 360°, so the following is true:

$2(m<1+m<2)+4(m<3+m<4)=360$

So:

$4(65)+4(m<3)=360$

This, since from properties of the rhombus m<3 = m<4, now we wil have:

$260+4(m<3)=360\Rightarrow4(m<3)=100$$\Rightarrow m<3=25$

Now, we will have the following:

$m<3=25$$m<4=25$

And finally, we can see that the measurement of angle 5 is:

$m<5=90$