Question

Please help! And show your work for each answer so I can understand, ty

Answer 1

a=17, R=101

Explanation:

10:

We know that if all angles of a triangle are congruent, the angles must be as well. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

We also know that all interior angles of a triangle add up to 180 degrees. If they are all equal this only leaves us with the possibility of every angle equaling 60 degrees, otherwise they wouldn't add up to 180 AND be equal simultaneously.

To find the value of a set the equation equal to 60.

`4a-8=60`

Solve for a:

`4a-8=60\\4a=68\\a=17`

19:

We know in a parallelogram all interior angles sum to 360 degrees.

Remember the sum of angle pairs between parallel lines is 180 degrees. Meaning if we add angles T and S and set them equal to 180 degrees we can then find the value of angle S as we would have the value of variable x.

`(4x+1)+(3x+4)=180\\7x+5=180\\7x=175\\x=25`

Now substitute in the known value of x to find angle S:

`3(25)+4\\75+4\\79`

Angle S measures 79 degrees.

Using our previous knowledge of two angles on a parallel line summing to 180 degrees, we can find the measure of angle R by subtracting 79 from 180.

`180-79=x\\101=x`

R=101