Which expression is equivalent to Measure of angle 4?

Question

A triangle has angles 1, 2, 3. The exterior angle to angle 1 is 4, to angle 2 is 5, to angle 3 is 6.
Measure of angle 2 + measure of angle 3
Measure of angle 1 + measure of angle 2
Measure of angle 1 + measure of angle 3
Measure of angle 5 + measure of angle 6 option 1 2 3 or 4

Answer 1

To find an expression equivalent to the measure of angle 4, we can use the properties of triangles and exterior angles.

In a triangle, the sum of the interior angles (angle 1, angle 2, and angle 3) is always equal to 180 degrees. The exterior angle (angle 4) is equal to the sum of the two opposite interior angles.

Thus:

• Measure of angle 4 = Measure of angle 2 + Measure of angle 3

Since this matches option 1, the correct answer is:

Option 1: Measure of angle 2 + measure of angle 3.