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KengaRu [80]3 years ago

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Please, Help. the answer isn't 30°

vagabundo [1.1K]

The missing angle of the right triangle ABC has a measure of 30°. (Correct answer: A)

<h3>How to find a missing angle by triangle properties</h3>

Triangles are geometrical figures formed by three sides and whose sum of internal angles equals 180°. There are two kind of triangles existing in this question: (i) Right triangles, (ii) Isosceles triangles.

Right triangles are triangles which one of its angles equals 90° and isosceles triangles are triangles which two of its sides have equal measures.

According to the statement, we know that triangle BQR is an isosceles triangle, whereas triangles ABC, ANB and NBC are right triangles. Based on the figure attached below, we have the following system of linear equations based on right triangles ABC and NBC:

2 · x + 90 + θ = 180 (1)

(90 - x) + 90 + θ = 180 (2)

By equalizing (1) and (2) we solve the system for x:

2 · x = 90 - x

3 · x = 90

x = 30

And by (1) we solve the system for θ:

θ = 180 - 2 · x - 90

θ = 30

The missing angle of the right triangle ABC has a measure of 30°. (Correct answer: A) $\blacksquare$