Question

I need help with angles and the measure of them i have abc a is 65 and b is (3x-10) and c is (2x) find the value of x

Answer 1

Step-by-step explanation:

There are three angles so it means this is a triangle and sum of all angles of a triangle is always 180°. These all angles add up to 180°.

65°+(3x-10)+(2x)=180°

Open the brackets:65°+3x-10+2x=180°

Arrange the numbers and valuables:65°-10°+3x+2x=180°

Calculate:55°+5x=180°

5x=180°-55°

5x=125°

x=125°÷5

x=25

Hence, Angle 1: 65°

Angle 2: 3x-10°

=3(25°)-10°

=65°

Angle 3: 2x

=2(25°)

=50°

Answer 2

Answer: x = 25

Step-by-step explanation:

The rule is that for any triangle, the three angles always add to 180 degrees

So A+B+C = 180

Replace A with 65, replace B with 3x-10 and replace C with 2x to get this new updated equation: 65 + 3x-10 + 2x = 180

Now let's isolate x

65 + 3x - 10 + 2x = 180

5x + 55 = 180 .................... combine like terms

5x + 55 - 55 = 180 - 55 ..... subtract 55 from both sides

5x = 125

5x/5 = 125/5 ..................... divide both sides by 5

x = 25

We can stop here since your teacher only wants to know the value of x.

-----------

If you're curious how to find the other angles, then replace x with 25 and compute

Angle B = 3x - 10 = 3*25 - 10 = 75 - 10 = 65 degrees

Angle C = 2*x = 2*25 = 50 degrees

Therefore, the three angles of the triangle are A = 65, B = 65, C = 50. As a check, they should add to 180. It turns out they do since A+B+C = 65+65+50 = 130 + 50 = 180. Therefore, the answer is confirmed.

note: since angles A and B are both the same at 65 degrees, this means the triangle is isosceles (the sides opposite the congruent angles are congruent sides). We do not have enough info to actually find the length of any of the three sides.