What is the Angled measurement of ∠B

The measurement of angle B is 50 degrees

Step-by-step explanation: we know all triangles add up to 180 degrees so substitute 40 with a degrees and solve

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 :) !!

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step-by-step explanation: