Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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°
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.