Answer: 117.6° ; 32.4° . _________________________ Explanation: _______________________________________________________ Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles. _____________________ We are given the following: _______________________ We have a triangle.
Angle 1: m∡1 = (8x) ;
Angle 2: m∡2 = (2x + 3) ;
Angle 3: m∡3 = 30. ______________________________________ We are asked to find: "m∡1" and " m∡2" . ______________________________________ Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees. ________________________________________ So, " m∡1 + m∡2 + m∡3 = 180 " . ________________________________________ Let us substitute our given values for the measurements in EACH of the THREE (3) angles — on the left-hand side of the equation; then solve for "x" ; then substitute that solved value for "x" into the given expressions for BOTH "m∡1" AND "m∡2" ; to find the values for " m∡1" AND " m∡2 " ; which are the values asked for in this very question ; ___________________________________________
m∡1 + m∡2 + m∡3 = 180 ; ___________________________________________ 8x + (2x + 3) + 30 = 180 ; ___________________________________________ 8x + 2x + 3 + 30 = 180 ; ___________________________________________ Combine the "like terms" on the 'left-hand side" of the equation; to simplify: ____________________________________________________________ +8x + 2x = +10x ; ___________________________________________ +3 + 30 = +33 ; ___________________________________________ Rewrite the entire equation, as: ___________________________________________ 10x + 33 = 180 ; ___________________________________________ Now, subtract "33" from EACH SIDE of the equation: ___________________________________________ 10x + 33 − 33 = 180 −<span> 33 ; ___________________________________________ to get: ___________________________________________ 10x = 147 ; ____________________________________________ Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" : ____________________________________________ 10x / 10 = 147 / 10 ; ____________________________________________ to get: ____________________________________________ x = 14.7 ; ___________________________________________ Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m</span>∡1" and "m∡2"; as follows: ________________________________________________
Angle 1: "(8x)" = 8*(14.7) = 117.6° ; ________________________________________________ Angle 2: "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ; ________________________________________________ These are the two answers; that is the 2 (TWO) values asked for in the question: 117.6° ; 32.4° . <span>____________________________________</span><span> Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m</span>∡3 = 30°); all add up to 180° ? ___________________________________________ Let us check: _______________________________ m∡1 + m∡2 + m∡3 = 180 ; _______________________________ Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true? ______________________________________________ → 117.6 + 32.4 + 30 = ? 180 ?? ______________________________________________ → 117.6 + 32.4 = 150 ; → 150 + 30 =? 180 ? Yes! ______________________________________________
