Question

Select from the drop-down menus to correctly complete the statements. By the triangle sum property, the sum of the measures of angles 2, 3, and 4 (90 or 180) is °. The sum of the measures of angles (1 and 2 or 1 and 4 or 2 and 3 or 3 and 4) is 180° because they form a linear pair. Using the substitution property, m∠2+m∠3+m∠4=m∠1+m∠4 . Then, by the subtraction property of equality, m∠2+m∠3=m∠ (4 or 1).

Answer 1

a) 180 degrees

b) angles 1 and 4

c) measure of Angle 1

Step-by-step explanation:

Step 1:

a)

We know that the sum of the 3 angles of a triangle is 180 degrees

From the diagram we know that the angles 2 3 and 4 are the angles of the given triangle

Hence the sum of the measures of the angles 2 3 and 4 is 180 degrees

Step 2 :

b)

The Angle in a straight line is 180 degrees. From the given diagram we can see that the angles 1 and 4 together forms a straight line. Hence they form a linear pair .so their sum is 180 degrees.

Step 3:

Given that sum of the measures of Angle 2 3 and 4 are equal to the sum of the measures of Angle 1 and 4. The sum of both the sets are equal to 180 degrees

Cancelling measure of Angle 4 on both sides, we have sum of the measure of Angle 2 and 3 is equal to measure of Angle 1