Question

1. TRIANGLES The ratios of the measures of the

angles in ADEF is 7:13:16.
F
16xº
E
137°
7x°
Find the measure of the angles

Answer 1

In triangle ADEF, the ratios of the measures of the angles are 7:13:16. By setting up an equation with the sum of the angles equal to 180 degrees, we can solve for the value of x and then find the measures of the angles.

Step-by-step explanation:

In triangle ADEF, the ratios of the measures of the angles are given as 7:13:16.

Let's assign variables to the angles. Let the measure of angle ADE be 7x, the measure of angle DEF be 13x, and the measure of angle EFA be 16x.

Since the sum of the angles in a triangle is 180 degrees, we can set up the equation 7x + 13x + 16x = 180 and solve for x.

Once we find the value of x, we can substitute it into the ratios to find the measures of the angles ADE, DEF, and EFA.

For example, if x is 5, then angle ADE is 7(5) = 35 degrees.

Answer 2

sum of all sides of triangle=180°

7x+13x+16x=180°

36x=180°

x=180°/36

x=5

angle D=7x

=7(5)

D=35°

angle E=13(x)

=13(5)

E=65°

angle F=16x

=16(5)

F=80°

angle D=35°

angle E=65°

angle F=80°