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

Answer:

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

Answer 2

Answer:

$m\angle CAT=45^{\circ}$

$m\angle TAD=135^{\circ}$

Step-by-step 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)

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

$7x+5=180$

$7x=180-5=175$

$x=\frac{175}{7}=25$

Substitute the values then we get

$m\angle CAT=2(25)-5=45^{\circ}$

$m\angle TAD=5(25)+10=125+10=135^{\circ}$