Question

Please help!

Triangle ABC has angle measures as shown. Show work. Complete sentence.




(a) What is the value of x?








(b) What is the measure of angle CBA?




(c) What is the measure of angle CAB?




(d) When these 3 interior angles of a triangle are added together, what does it equal?

Answer 1

9514 1404 393

Answer:

  (a) x = 22

  (b) 46°

  (c) 44°

  (d) 180°

Step-by-step explanation:

Because the sum of the interior angles of a triangle is 180°, we know that the sum of the acute angles in a right triangle is 90°.

(a)

The sum of the marked acute angles is 90°.

  2x +(3x -20) = 90

  5x = 110 . . . . . . . . . . add 20, collect terms

  x = 22 . . . . . . . . . divide by 5

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(b)

∠CBA = (3x -20)° = (3·22 -20)° = 46°

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(c)

∠CAB = 2x° = 2(22)° = 44°

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(d)

The sum of a triangle's interior angles is 180°.