Question

In the figure below, suppose m < 3 = 112° and m< 4 = 37°.

Answer 1

`\begin{gathered} \text{The sum of }the\text{ interior }angle\text{ }measures\text{ of }a\text{ triangle must be 180\degree} \\ \text{So, }m<2+m<3+m<4=180\text{ \degree} \\ m<3+m<4=112\text{ \degree+}37\text{ \degree} \\ m<3+m<4=149\text{ \degree} \\ m<2=180\text{ \degree-140\degree} \\ m<2=31\text{\degree} \\ From\text{ the figure, }we\text{ can s}ee\text{ }that\text{ m<1}+m<2=180\text{ \degree} \\ m<1=180\text{ \degree-31\degree} \\ m<1=149\text{ \degree} \\ \text{therefore, m<1=m<3+m<4} \\ \text{For any }triangle,\text{ the measure of }an\text{ exterior angle equals }the\text{ sum of } \\ \text{the measures of its two remote interior angles} \end{gathered}`