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The measure of the vertex angle of an isosceles triangle is (a + 30)°. The base angles each measure (2a - 15)°. What is the measure in degrees of one of the base angles?
  • a)
    36°
  • b)
    45°
  • c)
    57°
  • d)
    66°
  • e)
    90°
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The measure of the vertex angle of an isosceles triangle is (a + 30)&d...
The measure of the vertex angle of an isosceles triangle is always equal to (180 - 2a) degrees, where "a" is the measure of each base angle.
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Community Answer
The measure of the vertex angle of an isosceles triangle is (a + 30)&d...
To solve this problem, you must remember that in an isosceles triangle, the base angles have the same measure. Since the sum of angles is 180° for all triangles, 180 = (a + 30) + 2(2a -15). Distributing and adding like terms yields
180 = (a + 30) + 4a - 30
180 = 5a
a = 36
Since the base angles are equivalent to 2a - 15, they equal 2(36) - 15 = 72 - 15, or 57°.
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The measure of the vertex angle of an isosceles triangle is (a + 30)°. The base angles each measure (2a - 15)°. What is the measure in degrees of one of the base angles?a)36°b)45°c)57°d)66°e)90°Correct answer is option 'C'. Can you explain this answer?
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