Answer:
B
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180°
let the measure of B be x, then C = 2x - 18
the sum of the 3 angles is therefore
x + 2x - 18 + 90 = 180
3x + 72 = 180 ( subtract 72 from both sides )
3x = 108 ( divide both sides by 3 )
x = 36
Hence ∠B = 36°
The measure of ∠B is 36°, computed using the angle sum property of triangles. Hence, option B is the right choice.
According to the angle sum property of triangles, the sum of the three angles of any triangle is always equal to 180°.
If we have any triangle XYZ, then by the angle sum property of triangles, we can say that:
∠X + ∠Y + ∠Z = 180°.
In the question, we are informed that in the right triangle ABC, ∠A = 90°, and ∠C is 18° less than twice the measure of ∠B.
We are asked the measure of ∠B.
We are given that ∠C is 18° less than twice the measure of ∠B, that is,
∠C = 2(∠B) - 18°.
In the right triangle ABC, by the angle sum property of triangles, we can write that:
∠A + ∠B + ∠C = 180°.
Substituting the values of ∠A = 90° and ∠C = 2(∠B) - 18°, we get:
90° + ∠B + 2(∠B) - 18° = 180°.
To find the measure ∠B, we solve the above equation as follows:
90° + ∠B + 2(∠B) - 18° = 180°,
or, 72° + 3(∠B) = 180° {Simplifying},
or, 72° + 3(∠B) - 72° = 180° - 72° {Subtracting 72° from both sides of the equation},
or, 3(∠B) = 108° {Simplifying},
or, 3(∠B)/3 = 108°/3 {Dividing both sides of the equation by 3},
or, ∠B = 36°.
Thus, the measure of ∠B is 36°, computed using the angle sum property of triangles. Hence, option B is the right choice.
Learn more about the angle sum property of triangles at
https://brainly.com/question/22262639
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