Ask Question
12 August, 17:43

The angles in a triangle are such that one angle is 102∘ more than the smallest angle, while the third angle is 4 times as large as the smallest angle. Find the measures of all three angles.

+5
Answers (1)
  1. 12 August, 18:11
    0
    13 degrees, 115 degrees, and 52 degrees

    Step-by-step explanation:

    The addition of the three internal angles in a triangle should give 180 degrees.

    So let's name the angles A, B, C, with:

    A being the smallest angle

    B being the one that equals the smallest one plus 102 degrees. That is: B = A+102

    C being the one that is 4 times the smallest one. That is: C = 4 * A

    Now add the three to obtain 180, but writing all of them in terms of the smallest angle A:

    A + A + 102 + 4 A = 180

    2A + 4A + 102 = 180

    6 A + 102 = 180

    6 A = 180 - 102 = 78

    A = 78/6 = 13 degrees

    Therefore, angle B must be: A + 102 = 13 + 102 = 115 degrees

    C = 4 * A = 4 * 13 = 52 degrees
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “The angles in a triangle are such that one angle is 102∘ more than the smallest angle, while the third angle is 4 times as large as the ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers