Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

enter image description here

I've faced a question that needed to find angle $\gamma$ as a part of it and the solution came from $\gamma= \beta - \alpha$. How did the book arrive to such conclusion, and does this apply for every similar case?

share|improve this question

2 Answers 2

up vote 5 down vote accepted

The angle "next to" $\beta$ (supplementary to $\beta$) is $180^\circ-\beta$. The sum of the angles of a triangle is $180^\circ$, so $$\alpha+(180^\circ-\beta)+\gamma=180^\circ.$$

Remark: This is an often-used result. Usually it is stated as follows. The external angle ($\beta$) at a vertex is the sum of the internal angles at the other two vertices. So $\alpha+\gamma=\beta$.

share|improve this answer

total degrees in a triangle = 180

$$\beta_{supplement} = 180-\beta$$

so

$$180 = \gamma + \alpha + \beta_{supplement}$$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.