Answer:
The measure of angle ∠F is 102°.
Step-by-step explanation:
Given : Triangle DEF.
To find ∠F =?
Solution:
∠D = x
∠E = [tex]\frac{1}{2}[/tex]∠D = 0.5x
∠F = 2∠D -2 = 2x-2°
Applying angle sum property of the triangle:
∠D + ∠E + ∠F = 180°
[tex]x+0.5x+(2x-2^o)=180^o[/tex]
[tex]3.5x=180^o+2^o[/tex]
[tex]x=\frac{178^o}{3.5}[/tex]
x = 52
∠F = 2x-2° = 2 × 52° - 2° = 102°
The measure of angle ∠F is 102°.
