An exterior angle of an isosceles triangle has a measure of 110 degrees. find two possible sets of measures for the angles of the triangle.

40°, 70°, 70° . . . or . . . 55°, 55°, 70°

Step-by-step explanation:

If the given angle is exterior to one of the base angles, then that base angle must be 180°-110° = 70°. The other base angle will have the same measure, so the apex angle will be 180°-2·70° = 40°.

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If the given angle is exterior to the apex angle, that angle must be 70° and the base angles will each be 1/2 of 110°, or 55°.

Option A

The value of x in the equation 2(x - 3) + 5x = 5(2x + 6) is -12

Solution:

From question given that

2(x - 3) + 5x = 5(2x + 6)

Open the brackets,

2x – 6 + 5x = 10x + 30

Rewrite the above equation,

2x + 5x – 6 = 10x + 30

On simplifying the above equation, we get

7x – 6 = 10x + 30

Now adding 6 on both sides,

7x – 6 + 6 =10x + 30 + 6

7x = 10x + 36

On subtracting 10x on both sides,

7x - 10x = 10x + 36 - 10x

-3x = 36

On dividing -3 on both sides,

x = -12

Hence on simplifying 2(x - 3) + 5x = 5(2x + 6) we get value of x is -12. Hence Option (A) is correct.