Question

∠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

Answer 1

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

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

Answer 2

`m\angle CAT=45^(\circ)`

`m\angle TAD=135^(\circ)`

Explanation:

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

`m\angle CAT=2x-5`

`m\angle TAD=5x+10`

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

`m\angle CAT+m\angle TAD=180^(\circ)` (linear pair sum =180 degrees)

`2x-5+5x+10=180`

`7x+5=180`

`7x=180-5=175`

`x=(175)/(7)=25`

Substitute the values then we get

`m\angle CAT=2(25)-5=45^(\circ)`

`m\angle TAD=5(25)+10=125+10=135^(\circ)`