Question

Prove: m∠zab = m∠acb m∠cba triangle a c b is shown with its exterior angles. line a b extends through point x. line a c extends through point y. line c a extends through point x. we start with triangle abc and see that angle zab is an exterior angle created by the extension of side ac. angles zab and cab are a linear pair by definition. we know that m∠zab m∠cab = 180° by the . we also know m∠cab m∠acb m∠cba = 180° because . using substitution, we have m∠zab m∠cab = m∠cab m∠acb m∠cba. therefore, we conclude m∠zab = m∠acb m∠cba using the .

Answer 1

To prove that m∠zab equals the sum of m∠acb and m∠cba in triangle ABC, we use the linear pair property and interior angles sum property of triangles to show that the exterior angle equals the sum of the opposite interior angles.

Step-by-step explanation:

To prove that m∠zab = m∠acb + m∠cba for triangle ABC, we use the properties of exterior angles and linear pairs. Given that angles ZAB and CAB form a linear pair, we know their measures sum to 180°. Since the sum of the measures of angles inside triangle ABC, m∠cab + m∠acb + m∠cba, also equals 180°, we can create an equation using substitution:

m∠zab + m∠cab = m∠cab + m∠acb + m∠cba.

From this equation, by subtracting m∠cab from both sides, it simplifies to:

m∠zab = m∠acb + m∠cba.

This proves that the measure of the exterior angle ZAB is equal to the sum of the measures of the two non-adjacent interior angles (ACB and CBA) in the triangle.