Question

Find the measurements of each angle.

∆EFG and ∆LMN are supplementary angles, m∆EFG= (3x + 17)°, and m∆LMN= (1/2x - 5)°

∆EFG = ?

∆LMN = ?​

Answer 1

m∠EFG =
`161\°`

m∠LMN =
`19\°`

Explanation:

Given:

∠EFG and ∠LMN are supplementary angles

m∠EFG =
`(3x + 17)\°`

m∠LMN =
`((1)/(2)x - 5)\°`

We need to find m∠EFG and m∠LMN

Now we know that sum of the Supplementary angles are 180°

Hence we can say that;

m∠EFG + m∠LMN = 180°

Substituting the given values we get;

`(3x + 17)+ ((1)/(2)x - 5) = 180\\\\3x+17+(1)/(2)x-5 =180\\\\3x+(1)/(2)x-12=180\\\\3x+(1)/(2)x=180-12\\\\(3x*2)/(2)+(1)/(2)x = 168\\\\(6x+x)/(2) = 168\\\\7x = 168*2\\\\7x = 336\\\\x=(336)/(7)= 48`

Now Substituting the value of x to find the measures of angle;

m∠EFG =
`(3x + 17)\° = (3*48+17)\°= (144+17)\° =161\°`

m∠LMN =
`((1)/(2)x - 5)\°=((1)/(2)* 48 - 5)\°= (24 - 5)\°=19\°`