Story Problem

Question

The second angle of a triangle kite is four times as large as the first. The third angle is 5 degrees more than the sum of the other two angles. Find the measure of the second angle.

 

I know the answer is 70 degrees, but i want to know how they got that.

Answer 1

Hi Kendalyn 

we can mark to angle 1 as a1, angle 2 as a2 , and angle 3 as a3,

the problem states that

 a2 = 4*a1----->1

 a3= 5 + a1 + a2---->2

 also we now that sum of triangle's  angles = 180  means   a1 + a2 + a3 = 180----->3

substitute eq1 in eq 2 will have   a3 = 5 + a1 + 4*a1 ----> a3 - 5*a1 = 5   ----> 4 

also substitute  eq1 in eq 3 will have    a1 + 4*a1 + a3 = 180 ----> 5*a1 + a3 = 180---->5

now we can from eq4 and eq5 solve to find a1 

-a3 +5a1 = -5   (after multiply by -1)

a3 + 5a1 = 180

------------------

0 + 10a1 = 175------> a1 = 17.5 then

a2 = 4a1  -----> a2 = 4 * 17.5 ------> a2 = 70

 

best