Step-by-step explanation:
According to the Triangle Sum Theorem, all angles in triangle are sum of 180⁰. This means that m<a + m<b + m<c = 180⁰. You will first solve for a.
m<a + m<b + m<c = 180⁰
2a⁰ + a + 10⁰ + a⁰ = 180⁰ combine like terms.
2a⁰ + a + a⁰ + 10⁰ = 180⁰
4a⁰ + 10⁰ = 180⁰ subtract 10 from both sides.
4a⁰ + 10⁰ - 10⁰ = 180⁰ - 10⁰
4a⁰ = 170⁰ Divide 4 from both sides.
4a⁰ / 4 = 170⁰ / 4
a = 42.5⁰
Now that you found a, plug 42.5⁰ in place of in all angles and solve.
m<a :-
2a⁰
2(42.5)⁰
85⁰
m<b :-
a + 10⁰
42.5⁰ + 10⁰
52.5⁰
m<c :-
a⁰
42.5⁰
m<a = 85⁰
m<b = 52.5⁰
m<c = 42.5⁰
Remember that all angle must sum up to 180⁰ in a triangle. So we will now add all of our angle to find it if it equals 180⁰.
m<a + m<b + m<c = 180⁰
85⁰ + 52.5⁰ + 42.5⁰ = 180⁰
180⁰ = 180⁰
Thus, m<b = 52.5⁰.
Hope this helps, thank you :) !!
