contestada

7. In triangle ABC the measure of angle ABC is x ^ 2 the measure of angle BCA is - 6x + 100 and the measure of angle CAB is x + 56 . Find the measure of angle ABC

Respuesta :

Answer:

∠ ABC = 64°

Step-by-step explanation:

The sum of the 3 angles in triangle ABC = 180°

sum the 3 angles, equate to 180 and solve for x

x² - 6x + 100 + x + 56 = 180 ( simplify left side )

x² - 5x + 156 = 180 ( subtract 180 from both sides )

x² - 5x - 24 = 0 ← quadratic equation in standard form

(x - 8)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x + 3 = 0 ⇒ x = - 3

However, x > 0, then x = 8

Then

∠ ABC = x² = 8² = 64°

Otras preguntas