Question

5. In an isosceles triangle, each base angle is four times of its vertical angle. Find all the
angles of the triangle.
6. The vertical angle of an isosceles triangle is 15º more than each of its base angles
Find each angle of the triangle.
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Answer 1

Answer:

5- 80 degrees, 80 degrees, 20 degrees

6- 55 degrees, 55 degrees, 70 degrees

Step-by-step explanation:

5- let the vertical angle be 'x'

so the base angles, which are equal to each other = 4x

The sum of all angles of a triangle is always 180 degrees

so 4x + 4x + x = 180 degrees

so 9x = 180 degrees

so x = 180/9 = 20 degrees(vertical angle)

so 4x = 80 degrees (each of the base angles)

6- let the base angles, which are equal to each other = x

so the vertical angle = x + 15

by angle sum property of triangles, stated above,

x + x + (x+15) = 180 degrees

so 3x + 15 = 180

so 3x = 180 - 15 = 165 degrees

so x = 165/3 = 55 degrees

so x + 15 = 70 degrees

Hope it helps!! Stay safe!!