Question

Problem 4 the measure of the largest angle of a triangle is 90◦ more than the measure of the smallest angle, and the measure of the remaining angle is 30◦ more than the measure of the smallest angle. find the measure of each angle. showyourwork in obtaining your answe

Answer 1

Answer: The measurements of the angles are: 110° ; 50° ; 20° .
_________________________________________________________
Step-by-step explanation:
________________________________________________________
Note: There are 3 (three) angles in any triangle (by definition).

By definition, all the angles in any triangle add up to 180° .
________________________________________________________
The problems asks us to find the measure of EACH angle of the triangle.

We can set up an equation; given the information in the problem; to solve for the measure of EACH of the 3 (THREE) angles in the triangle:
________________________________________________________
→ " x + (x + 90) + (x + 30) = 180 " ;
_____________________________________________
in which: "x" is the measure of one of the angles;
(specifically, the smallest angle) in the triangle;
"(x + 90)" is the measure of another one of the angles in the triangle;
"(x + 30)" is the measure of another one of the angles in the triangle;
___________________________________________________________
By solving for "x" in the equation; we can solve for the measures of all the angles in the triangle;
_________________________________________________
→ x + (x + 90) + (x + 30) = 180 ;

x + x + 90 + x + 30 = 180 ;

→ 3x + 120 = 180 ;
______________________________________
Subtract "120" from each side of the equation ;

3x + 120 − 120 = 180 − 120 ;

to get: 3x = 60 ;
________________________________
Now, divide EACH SIDE of the equation by "3" ; to isolate "x" on one side of the equation ; and to solve for "x" ;

3x = 60 ;

3x / 3 = 60 / 3 ;

x = 20 ;
_________________________________________
Now, we have the original equation:
__________________________________
x + (x + 90) + (x + 30) = 180 ;

in which: x = 20° {the smallest angle) ;
"(x + 90)" = "(20 + 90) = 110° ;
"(x + 30)" = "(20 + 30)" = 50° ;
__________________________________________________________
Answer: The measurements of the angles are: 110° ; 50° ; 20° .
__________________________________________________________
To check our work:

20 + 110 + 50 =? 180 ?? ; → 130 + 50 =? 180 ?? ; → Yes!
_____________________________________________________