The angles in a triangle are such that one angle is 100 degrees more than the smallest angle, while the third angle is 2 times as large as the smallest angle. Find the measures of all three angles.
Accepted Solution
A:
Answer:The measure of the three angles are 120°, 20° and 40°Step-by-step explanation:Letx ----> the measure of the first angley ---> the measure of the second angle (smallest angle)z ---> the measure of the third angleRemember thatThe sum of the angles in a triangle must be equal to 180 degreesso[tex]x+y+z=180[/tex] ----> equation A[tex]x=y+100[/tex] -----> equation B[tex]z=2y[/tex] ------> equation Csolve the system by substitutionsubstitute equation B and equation C in equation A[tex](y+100)+y+(2y)=180[/tex]solve for y[tex]4y+100=180[/tex][tex]4y=180-100[/tex][tex]4y=80[/tex][tex]y=20\°[/tex]Find the value of x[tex]x=y+100[/tex] ---- [tex]x=20+100=120\°[/tex] Find the value of z[tex]z=2y[/tex] ----> [tex]z=2(20)=40\°[/tex]thereforeThe measure of the three angles are 120°, 20° and 40°