Question

Please help!!

The sum of the interior angle measures must be __ ?

So m<1 + m<3 + m<4 = __

We are given m<1 = 32

So, m<3 + m<4 = __ ?

From the figure, we can see that m<1 + m<2 = ___

Since m<1 = 32, it must mean that m<2 = __ ?

Answer 1

180, 180, 148, 180, 148

Explanation:

The two rules in play here are ...

• the sum of interior angles of a triangle is 180°
• the angles of a linear pair are supplementary (they total 180°)

__

The first of these rules answers the first two questions:

• interior angles total 180°
• angles 1, 3, 4 total 180°

We can subtract the measure of angle 1 from both sides of the previous equation to find the sum of the remaining two angles.

• angles 3 and 4 total 148°

The second rule answers the next question:

• angles 1 and 2 total 180°

As before, subtracting the value of angle 1 from both sides of the equation gives ...

• angle 2 must be 148°

_____

Additional comment

Of course, the subtraction property of equality comes into play, also. For some unknown, X, you have (in both cases) ...

X + 32° = 180°

X +32° -32° = 180° -32° . . . . . . subtraction property of equality

X = 148° . . . . . . . . simplify

In the first case, X is the sum of angles 3 and 4. In the second case, X is angle 2 only.