∠cat and ∠tad are a linear pair, if m∠cat = 2x-5 and m∠tad = 5x+10, what is the measure of ∠cat and ∠tad? draw a picture labelling the given information and show your work

The answer to your question is: m∠CAT = 45;  m∠TAD = 135

Step-by-step explanation:

Data

∠CAT and ∠TAD are a linear pair

m∠CAT = 2x-5

m∠TAD = 5x+10

m∠CAT = ?

m∠TAD = ?

Process

The sum of linear pairs angles equals 180°, so

                         m∠CAT + m ∠TAD = 180°

                         (2x - 5)  + (5x + 10) = 180°

                         2x - 5 + 5x + 10 = 180

Solve for x        7x + 5 = 180

                         7x = 180 - 5

                         7x = 175

                         x = 175 / 7

                         x = 25

m∠CAT = 2(25) - 5 =  50 -5 = 45

m∠TAD = 5(25) + 10 = 125 + 10 = 135

Step-by-step explanation:

We are given that angle CAT and angle TAD are a linear pair.

We have to find the measure of angle CAT and angle TAD.

 (linear pair sum =180 degrees)

Substitute the values then we get

7.3

step-by-step explanation: