Question

The two
parallelogram
| Find all
parallelogrom
con interior angles
are 3x-S2 and
the angle of
of a
sx - 2015
the​

Answer 1

Step-by-step explanation:

Every triangle has 6 exterior angles, two at each vertex.

• Angles 1 through 6 are exterior angles.

• Notice that the "outside" angles that are "vertical" to the angles inside the triangle are NOT called exterior angles of a triangle.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

(Non-adjacent interior angles may also be referred to as remote interior angles.)

FACTS:

• An exterior ∠ is equal to the addition of the two Δ angles not right next to it.

140º = 60º + 80º;        120º = 80º + 40º;

100º = 60º + 40º

• An exterior angle is supplementary to its adjacent Δ angle. 140º is supp to 40º

• The 2 exterior angles at each vertex are = in measure because they are vertical angles.

• The exterior angles (taken one at a vertex) always total 360º

Examples:

1. 

Solution: Using the Exterior Angle Theorem

145 = 80 + x

x = 65

Now, if you forget the Exterior Angle Theorem, you can still get the answer by noticing that a straight angle has been formed at the vertex of the 145º angle. See Example 2.

2. 

Solution: I forgot the Exterior Angle Theorem.

The angle adjacent to 145º will form a straight angle along with 145º adding to 180º. That angle is 35º.

Now use rule that sum of ∠s in Δ = 180º.

35 + 80 + x = 180

115 + x = 180

x = 65

3. 

Find m∠DBC.

Solution:∠BDC is an exterior angle for ΔABD.

m∠BDC = 35 + 25

m∠BDC = 60º

180 = m∠DBC + 60 + 60

m∠DBC = 60º

4. 

Find xº.

Solution:

100 = x + 50

x = 50º