Question

Hello, happy Friday, I am just here with some geometry questions.

Answer 1

Answer:

m∠D = 29°

Step-by-step explanation:

First, notice that ΔSTU and ΔDEF are similar triangles.

For instance, for side ST and DE, the scale factor is:

$\displaystyle k=\frac{6}{15}=\frac{2}{3}$

Likewise, for TU and EF and SU and DF, the scale factor reamins that same:

$\displaystyle \frac{10}{4}=\frac{2}{5}\text{ and } \frac{8}{20}=\frac{2}{5}$

By SSS Similarity, ΔSTU ~ ΔDEF.

Note that our similarity statement states that ∠S corresponds to ∠D.

So, ∠S = ∠D.

Since the angles remain the same in a scaled factor and ∠S measures 29°, ∠D is also 29°.

Answer 2

Answer:

m<D = 105

Step-by-step explanation:

So, Triangle STU and DEF are similar triangles, because their corresponding side lengths have the same ratio.

For example FD can be multiplied by 2.5 to get SU, and EF can be multiplied by 2.5 to get TU, and ED can me multiplied by 2.5 to get 15.

Anyways, since the two triangles are similar, they have the same angle measures, meaning that angle D can be found by subtracting 46 and 25 from 180 degrees to find the missing angle, which is 105 degrees. I hope that helps.