Question

2. One angle of a triangle measures 10 degrees more than the second. The measure of the third angle is twice the sum of the measures of the first two angles. Find the measure of each angle. [Hint: the sum of the three angles in a triangle equals 180°.] PLEASE SHOW YOUR WORK I WILL MAKE BRAINLIST PLEASE!!!!!!!

Answer 1

Answer:

first angle = 25 degrees

Second angle = 35 degrees

Third side = 120/degrees

Step-by-step explanation:

Let the size of the second angle be x degrees.

One angle of a triangle measures 10 degrees more than the second. This means that the size of the first angle is ( x+ 10 )degrees.

The measure of the third angle is   twice the sum of the measures of the first two angles. This means that   The third angle = 2( first angle + second angle). So the size of each angle is  

First angle (x + 10) degrees  

Second angle = x degrees

Third angle = 2(x + 10 + x) =  (4x + 20) degrees

Sum of angles in a triangle = 180  degrees. Therefore,  x + 10 + x + 4x + 20 = 180 degrees  6x + 30 = 180

6x = 180 - 30 = 150

x = 150/6 = 25 degrees

First angle = x + 10 = 25 +10 = 35

Third angle = 4x + 20 = 4 × 25 + 20

= 100+ 20 = 120 degrees

Hope this helps

Answer 2

Answer:25(1st angle),35(2nd angle),120(3rd angle)

Step-by-step explanation: (/ stands for divide)

180/6=30 (sum of angles/total units=value of one unit, third angle is 4 units as it is twice the sum of first two angles)

30x4=120 (value of unitxnumber of units of 3rd angle=3rd angle)

30x2=60 (value of unitxfirst angle+second angle total units=value of 1st angle+2nd angle)

(60-10)/2=25(1st angle)

25+10=35(2nd angle)

CHECK: 35+25+120=180

hope you get it :)