Question

How do I do this? What do I do with the 68 and 79 on each?

Answer 1

hello

solve the first problem, we are to find the missing angle

to solve for x, i had to make up new characters to find missing sides

first of all, let's solve for y

`\begin{gathered} 45+y=180 \\ \text{reason:angle on a straight line is equal to 180 degr}e \\ y=180-45=135^0 \end{gathered}`

let's use this knowledge to solve for z

`\begin{gathered} y+z=180 \\ \text{reason: angles on a straight line = 180} \\ 135+z=180 \\ z=45^0 \end{gathered}`

note: z= 45, we can as well use opposite angles are equal theorem

we should solve for angle a now

`\begin{gathered} 60+z+a=180^0 \\ \text{reason:sum of angles in a triangle is equal to 180 degre}es \\ 60+45+a=180 \\ 105+a=180 \\ a=180-105 \\ a=75^0 \end{gathered}`

we ca use the knowledge of a to solve for b

`\begin{gathered} a+68+b=180^0 \\ \text{reason:angles on a straight line is equal to 180 degr}ees \\ 75+68+b=180_{} \\ 143+b=180 \\ b=180-143 \\ b=37^0 \end{gathered}`

let's use the value of b to solve for c

`\begin{gathered} b+100+c=180^0 \\ \text{reason:sum of angles in a triangle is equal to 180 degre}e \\ 37+100+c=180 \\ 137+c=180 \\ c=180-137 \\ c=43^0 \end{gathered}`

finally, we can solve for x

`\begin{gathered} c+x=180^0 \\ c=43^0 \\ 43+x=180 \\ x=180-43 \\ x=137^0 \end{gathered}`

the value of the unknown angle is equal to 137 degrees