Question

Find the measures of angles of triangle DEF

Answer 1

Angle E = 90°

Angle D= 55°

Angle F = 35°

Sum of all the angles of a triangle = 180° ( angle sum property).

Angle D + Angle E + Angle F = 180°

8x - 1 + 5x + 90° = 180°

8x + 5x + 89 = 180

13x = 180 - 89

13x = 91

x = 7.

Angle D = 8x - 1

= 8(7)-1

= 56 - 1

= 55

Angle E = 90° ( given)

Angle F = 5x

= 5 * 7

= 35

Answer 2

m∠E: 90°

m∠D: 55°

m∠F: 35°

Explanation:

Since the interior angles of a right triangle sum up to 180°, the sum of angles D, E, F will equal 180°. We can then form an equation from that information.

`90+(8x-1)+5x=180\\13x-1=90\\13x=91\\x=7`

From this, we can plug in the variable.

`mE=90\\mD=55\\mF=35`