Question

In Triangle DEF, if angle D is congruent to angle E, DE= x + 4, EF= 4x - 8, and DF= 7X - 35 find X and the measure of each side

Answer 1

Find out X and the measure of each side.

To proof

the diagram is given below

As given

angle D is congruent to angle E,

thus by using the property

if the two angle are equal to eachother than their opposite sides are also equal.

i.e

EF = DF

as given

DE= X + 4, EF= 4X - 8, DF = 7X-35

thus

4X -8 = 7X -35

solve

-3X = -27

`X = (27)/(3)`

X = 9

therefore

DE= X + 4

= 9 + 4

= 13 unit

EF= 4X - 8

= 36 -8

= 28 unit

DF= 7X - 35

= 63 -35

= 28 unit

Hence proved