what is ( mangle abc )?\n( mangle abc = 15^{circ} )\n( mangle abc = 45^{circ} )\n( mangle abc = 60^{circ}…

what is ( mangle abc )?\n( mangle abc = 15^{circ} )\n( mangle abc = 45^{circ} )\n( mangle abc = 60^{circ} )\n( mangle abc = 75^{circ} )

what is ( mangle abc )?\n( mangle abc = 15^{circ} )\n( mangle abc = 45^{circ} )\n( mangle abc = 60^{circ} )\n( mangle abc = 75^{circ} )

Answer

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. In (\triangle ABC), the exterior angle at (C) is (135^{\circ}), and the two non - adjacent interior angles are (\angle A) and (\angle ABC). Let (m\angle ABC=x). Then, by the exterior - angle theorem, (135^{\circ}=\angle A + x).

Step2: Substitute the value of (\angle A)

We know that (\angle A = 75^{\circ}). Substituting (\angle A = 75^{\circ}) into the equation (135^{\circ}=\angle A + x), we get (135^{\circ}=75^{\circ}+x).

Step3: Solve for (x)

To find (x) (which is (m\angle ABC)), we use the subtraction property of equality. Subtract (75^{\circ}) from both sides of the equation: (x=135^{\circ}-75^{\circ}).

[x = 60^{\circ}]

Answer:

(m\angle ABC = 60^{\circ})