Answer:
m<E = 105°
Explanation:
The ratio of the corresponding side lengths of ∆STU and ∆DEF are equal. That is:
[tex] \frac{ST}{DE} = \frac{TU}{EF} = \frac{SU}{DF} = \frac{15}{6} = \frac{10}{4} = \frac{20}{8} = 2.5 [/tex].
According to similarly theorem, if two ∆s are similar, the ratio of their corresponding lengths would be the same. Therefore, ∆STU is similar to ∆DEF.
Since ∆STU ~ ∆DEF, their corresponding angles are congruent. That is:
<S ≅ <D, this means both are 29° each.
<T ≅ <E, this means they are both equal
<U ≅ <F. this means both are 46° each.
Thus:
m<E = 180 - (m<D + m<F) (sum of ∆)
m<E = 180 - (29 + 46) (substitution)
m<E = 180 - 75
m<E = 105°
