Question

A pennant is in the shape of an isoseceles traingle. One leg of the traingle is fastened to a stick so that the bottom leg of the traingle make a 68 degrees exterior angle with the stick. what is the measure of each remote interior angle?

Answer 1

Draw a figure representing that situation:

Since the angle A and the angle of 68° are supplementary angles, then:

`A+68=180`

Substract 68 from both sides of the equation to find A:

`A=112`

Since the sum of the interior angles of a triangle is always 180, then:

`\begin{gathered} A+B+B=180 \\ \Rightarrow A+2B=180 \end{gathered}`

Substitute for A=112:

`112+2B=180`

Substract 112 from both sides of the equation:

`2B=68`

Divide both sides of the equation by 2:

`B=34`

Therefore, the measure of both remote angles is 34°.

(Both have the same measure, since it is an isosceles triangle).