Answered

Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

The sum of the measures of any two complementary angles is 90°. The differencebetween the measures of two specific complementary angles is 46. What is themeasure of each angle? Enter them below, separated by a comma. Write "deg" for thedegree symbol.Pls see the picture

The Sum Of The Measures Of Any Two Complementary Angles Is 90 The Differencebetween The Measures Of Two Specific Complementary Angles Is 46 What Is Themeasure O class=

Sagot :

[tex]\alpha=68^{^{\circ}},\beta=22^{\circ}[/tex]

1) We can tackle this question by setting a system of Linear equations for these angles.

2) Let's set that and solve it by the Method of Elimination.

[tex]\mleft\{\begin{matrix}\alpha+\beta=90^{\circ} \\ \alpha-\beta=46^{\circ}\end{matrix}\mright.[/tex]

Note that we are considering the same angles from the 1st equation as in the second. The 1st equation is the definition of complementary angles.

[tex]\begin{gathered} \mleft\{\begin{matrix}\alpha+\beta=90^{\circ} \\ \alpha-\beta=46^{\circ}\end{matrix}\mright. \\ \alpha+\beta=90^{\circ} \\ \alpha-\beta=46^{\circ} \\ --------- \\ 2\alpha=136^{\circ} \\ \frac{2\alpha}{2\alpha}=\frac{136}{2} \\ \alpha=68^{\circ} \\ \\ ---- \\ \alpha+\beta=90^{\circ} \\ 68^{^{\circ}}+\beta=90^{\circ} \\ \beta=90^{\circ}-68^{\circ} \\ \beta=22^{^{\circ}} \end{gathered}[/tex]

Note that after finding alpha we could plug into one of those equations and find beta.

Thus that's the answer.

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.