Answered

Join IDNLearn.com today and start getting the answers you've been searching for. Ask any question and receive timely, accurate responses from our dedicated community of experts.

Please explain https://brainly.com/question/12728473How 5x is the measure of the external angle opposite that internal angle and angle 2x of ΔABCExact Exercise: Find the value of x in each case. Give reasons to justify your solutions!

Please Explain Httpsbrainlycomquestion12728473How 5x Is The Measure Of The External Angle Opposite That Internal Angle And Angle 2x Of ΔABCExact Exercise Find T class=

Sagot :

Explanation

Step 1: Alternate interior angles) Let's see the following picture.

The head arrows on the segments DC and AB mean that both are parallel. Then, orange angles are alternate interior angles, which implies that both are equal. Then, we have

Step 2: Exterior angle theorem) Now, there is a very useful property of exterior angles. It says that every exterior angle of a triangle is the sum of its "opposite" interior angles:

In our present case, this theorem leads us to

[tex]5x=33+2x\text{.}[/tex]

Solving this equation for x, we get

[tex]\begin{gathered} 5x=33+2x, \\ 5x-2x=33, \\ 3x=33, \\ x=11. \end{gathered}[/tex]Answer[tex]x=11[/tex]

View image TalionG738247
View image TalionG738247
View image TalionG738247
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.