Question

46°

Answer 1

Answer:

m ∠D = 29°

m ∠T  = 105°

Step-by-step explanation:

Given: ΔSTU and ΔDEF

To find: m ∠D and m ∠T

Solution:

According to SSS similarity criteria,

two triangles are said to be similar if their corresponding sides are proportional.

In ΔSTU and ΔDEF,

$\frac{ST}{DE}=\frac{15}{6}=\frac{5}{2} \\\\\frac{TU}{EF}=\frac{10}{4}=\frac{5}{2}\\\\\frac{SU}{DF}=\frac{20}{8}=\frac{5}{2}$

So,

$\frac{ST}{DE}=\frac{TU}{EF}=\frac{SU}{DF}=\frac{5}{2}$

Therefore,

ΔSTU ≈ ΔDEF

If two triangles are similar then measure of their corresponding angles are equal.

m ∠D = m ∠S = 29°

m ∠U = m ∠F = 46°

In ΔSTU,

m ∠S + m ∠T + m ∠U = 180°

29° + m ∠T + 46° = 180°

75° + m ∠T = 180°

m ∠T  = 180° - 75° = 105°

(According to angle sum property of a triangle, sum of measures of angles of a triangle is equal to 180°)