Question

find the values of x and y.
(5x + 9)°
(4y)°
(5y - 1)°
116°
x =
y =

Explanation:

Step1: Use angle - addition property

We know that the sum of angles on a straight - line is 180°. Since ∠EHF = 116° and ∠EHD=(4y)° and ∠DHC=(5x + 9)° and ∠CHF = 180°, and also ∠EHF=(5y - 1)°+116°. So, (5y - 1)+116 = 180.
(5y - 1)+116=180
5y+115 = 180
5y=180 - 115
5y = 65
y = 13

Step2: Find the value of x

We know that vertical angles are equal. ∠DHC and ∠EHF are vertical angles. ∠EHF = 116°+(5y - 1)°. Substitute y = 13 into ∠EHF, we get ∠EHF=116+(5×13 - 1)=116 + 64=180°. Also, ∠DHC=(5x + 9)° and ∠EHF are vertical angles. So, 5x+9=64.
5x+9 = 64
5x=64 - 9
5x = 55
x = 11

Answer:

x = 11
y = 13