Question

Given: δabc 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

The student's question concerns proving an equality between an exterior angle of a triangle and the sum of two interior, non-adjacent angles, relying on the properties of angles in triangles and the exterior angle theorem.

Step-by-step explanation:

The question deals with geometric principles, specifically the properties of angles within a triangle and the exterior angles. In a triangle, the sum of the interior angles is always equal to 180 degrees. When an exterior angle is formed by extending one of the sides of a triangle, it is equal to the sum of the two non-adjacent interior angles. This is known as the exterior angle theorem.

The problem involves proving that m∠ZAB = m∠ACB + m∠CBA, which is based on the understanding that m∠ZAB + m∠CAB = 180° and m∠CAB + m∠ACB + m∠CBA = 180°. By substituting and simplifying, we can prove the required equality.