Question

Isosceles triangle- angle a is 3x-6 and angle c is 2x. What is the value of x

Answer 1

Isosceles triangle- angle a is 3x-6 and angle c is 2x. What is the value of x

Solution:

It has two cases:

If angle $A =$ angle $B$ , we have next equation:

$(3x - 6)*2 + 2x = 180$

Let's solve it:

$8x - 12 = 180$

$8x = 192$

$x = 24$

Then $A = B = 3 * 24 - 6 = 66{}^{\circ}, C = 2 * 24 = 48{}^{\circ}; 66 + 66 + 48 = 180{}^{\circ} - \text{Correct}$

If angle $C =$ angle $B$ , we have next equation:

$(3x - 6) + 2x * 2 = 180$

Let's solve it:

$7x - 6 = 180$

$7x = 186$

$x = 26.57$

Then $C = B = 2 * x = 53.14{}^{\circ}, A = 3 * 26.57 - 6 = 73.72{}^{\circ}; 53.14 + 53.14 + 73.72 = 180{}^{\circ} - \text{Correct}$

Answer $x = 24$ ; $x = 26.57$