Question

If triangle CAT ~ triangle DOG, angle C = 70, angle T = x + 12, angle D = 7x, then find angle T

Answer 1

To find the measure of angle T in triangle CAT, set up a proportion with the corresponding angles in triangle DOG. Solve the resulting equation to find the value of x, and then substitute that value into the expression for angle T. The answer is 12 degrees.

Step-by-step explanation:

Given that triangle CAT is similar to triangle DOG, we can determine the measure of angle T by setting up a proportion with the corresponding angles:

Angle C in triangle CAT corresponds to angle D in triangle DOG, so we have:

70 / (x + 12) = 7x / x

Cross multiplying gives us:

70x = 7x(x + 12)

Simplifying, we get:

70x = 7x^2 + 84x

Combining like terms:

0 = 7x^2 + 14x

Factoring out x:

0 = 7x(x + 2)

Setting each factor equal to zero gives us two possible values for x:

x = 0 or x = -2

Since angle T cannot be negative, we can conclude that x = 0. Therefore, angle T can be determined by substituting x = 0 into the expression for angle T:

angle T = x + 12 = 0 + 12 = 12