Question

Madison drew angle DEF In her triangle, angle d is represented as x degrees. The measure of Angle E is half the measure of angle  D. The measure of angle F is 2 degrees less than twice angle  D. What is angle F?

Answer 1

D = x
E = .5x
F = 2x-2

(x)+(.5x)+(2x-2)=180
3.5x-2=180
3.5x=182
x=52

F = 2(52)-2 = 102 degrees

Answer 2

The measure of angle ∠F is 102°.

Explanation:

Given : Triangle DEF.

To find ∠F =?

Solution:

∠D = x

∠E =
`(1)/(2)`∠D = 0.5x

∠F = 2∠D -2 = 2x-2°

Applying angle sum property of the triangle:

∠D + ∠E + ∠F = 180°

`x+0.5x+(2x-2^o)=180^o`

`3.5x=180^o+2^o`

`x=(178^o)/(3.5)`

x = 52

∠F = 2x-2° = 2 × 52° - 2° = 102°

The measure of angle ∠F is 102°.