Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

The measures of the angles of a triangle are in the extended ratio 2:2:8. What is the measure of the smallest angle?

Sagot :

sugarmate


Let the three angles of the triangle be represented by 2x, 2x, and 8x.

2x + 2x + 8x = 180

x = 15 and 2x = 30.

The angles of the triangle are 30, 30, and 120.

The smallest angle has measure 30.

Note that  30:30:120 is equivalent to the given ration 2:2:8

Gwenuin
We know that the ratio is;

[tex]2:2:8[/tex]

The angles in a triangle add up to give 180°

We can think of there being twelve "parts" that add up to 180°

[tex]2x + 2x + 8x = 180 \\ \\ 12x = 180 \\ \\ x = \frac{180}{12} \\ \\ x = 15 [/tex]

So our ratio is;

[tex]2*15 : 2*15 : 8*15 \\ \\ = 30 : 30 :120[/tex]

So the smallest angle is 30°
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.