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,
[tex]\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}[/tex]
So,
[tex]\frac{ST}{DE}=\frac{TU}{EF}=\frac{SU}{DF}=\frac{5}{2}[/tex]
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°)
