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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
.

Sagot :

Raphealnwobiidn

m∠ZAB + m∠CAB = 180° by the angle addition postulate

m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem

m∠ZAB = m∠ACB + m∠CBA using the subtraction property

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

m∠ZAB + m∠CAB = 180° by the angle addition postulate

m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem

m∠ZAB = m∠ACB + m∠CBA using the subtraction property

Find out more on equation at: https://brainly.com/question/2972832

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Issebearidn

Answer:

Angle addition postulate, triangle angle sum theorem, subtraction property

Step-by-step explanation:

Correct on edg

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