Question

A triangle XYZ is congruent to triangle FED. Find the measure of the indicated angle X is (5x+8)° , angle Y is (7x)° and angle Z is (6x-4)?

Answer 1

All angles in a triangle are supplementary..

x+y+Z=180
5x+8+7x+6x-4=180
18x+4=180
18x=180-4
18x=176
x=176/18
x=9.77
5(9.77)+8=56.88
7(9.77)=68.39
6(9.77)-4=54.62

Answer 2

$<b><u><i>$ Given :

∆ XYZ congruent to ∆ FED

X° = ( 5x + 8 )°

Y° = ( 7x )°

Z° = ( 6x - 4 )°

Find :

X°, Y°, Z°

We know that, Sum of all Angles of a Triangle = 180°

So,

X° + Y° + Z° = 180°

Putting the values of X°, Y°, Z°

( 5x + 8 )° + ( 7x )° + ( 6x - 4 )° = 180°

Removing brackets

5x + 8 + 7x + 6x - 4 = 180°

5x + 7x + 6x + 8 - 4 = 180°

18x + 4 = 180°

18x = 180 - 4

18x = 176

x = 176/18

x = 9.77

x = 9.8 ( approximate value )

Finding values

$= > x = (5x + 8) \\ \\ = > x = 5 \times \frac{98}{10} + 8 \\ \\ = > x = 49 + 8 \\ \\ = > x = 57$
______________

$= > y = 7x \\ \\ = > y = 7 \times \frac{98}{10} \\ \\ = > y = 68.6$
_______________

$= > z = 6x - 4 \\ \\ = > z = 6 \times \frac{98}{10} - 4 \\ \\ = > z = 58.8 - 4 \\ \\ = > z = 54.8$


Thanks!