Work out the size of angle ABC.
In a triangle, angle A is 35 degrees and angle C is 25 degrees. Find the value of angle B.
Answer (2)
The size of angle ABC is 120 degrees, calculated by using the triangle angle sum property. This is done by adding the known angles (A and C) and subtracting from 180 degrees. Thus, angle B is found to be 120 degrees.
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To find the size of angle ∠ A BC in the triangle, we will use the fact that the sum of the angles in a triangle is always 18 0 ∘ .
Here's how we can find ∠ B :
We know that in any triangle, the sum of the three angles is 18 0 ∘ . Therefore, we have: ∠ A + ∠ B + ∠ C = 18 0 ∘
From the problem, we know ∠ A = 3 5 ∘ and ∠ C = 2 5 ∘ .
Substitute the known values into the equation: 3 5 ∘ + ∠ B + 2 5 ∘ = 18 0 ∘
Combine the known angles: 6 0 ∘ + ∠ B = 18 0 ∘
To find ∠ B , subtract 6 0 ∘ from 18 0 ∘ : ∠ B = 18 0 ∘ − 6 0 ∘ = 12 0 ∘
Therefore, the size of angle ∠ A BC is 12 0 ∘ .
