In Δ ABC, angle B is 2.5 times angle A, and angle C is 24 ° less than angle B. Find angle C.

| March 12, 2021 | education

To find the value of the angle C, first assume that the angle A is x degrees.
Then the angle B is 2.5x degrees.
Now let’s express what the angle C is equal to.
Its magnitude is 2.5x – 24 degrees.
Next, recall the rule that the sum of the angles in a triangle is 180 °.
For a given triangle ABC, write the following expression.
A + B + C = 180 °.
Now we successively substitute the previously compiled designations for the angles A, B and C into this expression, for convenience omitting the designations of degrees.
x + 2.5x + (2.5x – 24) = 180.
Next, you should first open the brackets, give similar ones and solve the resulting equations.
x + 2.5x + 2.5x – 24 = 180.
6x = 180 + 24.
6x = 204.
x = 204: 6.
x = 34 ° – angle A.
Now let’s find the value of the angle C.
2.5x – 24 = 2.5 × 34 – 24 = 85 – 24 = 61 ° – angle C.
Thus, the answer given under the letter C is correct.
Answer: 61 °.



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