MATH SOLVE

5 months ago

Q:
# In a triangle, the measure of the second angle is twice the measure of the first angle. the third angel is equal to the sum of the other angels

Accepted Solution

A:

Answer:So the angles have measurements 30,60, and 90 degrees. Step-by-step explanation:We have a triangle which means the interior angles of that triangle has sum 180 degrees.Let's call the angle measurements: A, B, and C.A+B+C=180B=2A (The second angle is twice the first.)C=A+B (The third angle is the sum of the other 2.)If C=A+B, then C=A+2A (since B=2A).So we have this system:A+B+C=180B=2AC=3A (since C=A+2A=3a).Now I'm going to use the first equation A+B+C=180 and plug in the other equations we have below it:A+B+C=180 with B=2A and C=3A.A+2A+3A=1806A=180 Divide both sides by 6:A=180/6A=30If B=2A and A=30, then B=2(30)=60.If C=3A and A=30, then C=3(30)=90.So the angles have measurements 30,60, and 90 degrees.