Exterior Angle Theorem

Q. Sum of two opposite interior angles of a triangle is equal to it's angle.

1. exterior
2. interior
3. right

Q.

An exterior angle of a triangle is always greater than either of the interior opposite angles.

1. True

2. False

Q.

An exterior angle of a triangle is equal to the sum of the two interior opposite angles.

1. True

2. False

Q.

The exterior angle of a triangle is greater than both the interior opposite angles.

1. True

2. False

Q.

The exterior angle of a triangle is equal to ___________.

1. Sum of all interior angles

2. Sum of interior opposite angles

3. Insufficient data

4. The other exterior angle

Q. The sum of the lengths of any 2 sides of a triangle is ____ the length of the third side.

1. unrelated to
2. greater than
3. smaller than
4. equal to

Q. The ratio of the sides AB : BC : AC is equal to

1. 5 : 13 : 12
   
2. 12 : 13 : 5
   
3. 5 : 12 : 13
   
4. 13 : 5 : 12

Q.

The value of the exterior angle of a triangle is equal to the sum of __?

1. the two interior opposite angles

2. the other two exterior angles of a triangle

3. all the interior angles of a triangle

4. the value of external angles of a triangles cannot be found

Q.

Which one of the following is/are correct?

1. x + y + z = A + z

2. x + y + z = A

3. 2A > x + y

4. A > x + y

Q.

In the given figure,
$\angle CAE={84}^{\circ }$.
If $\angle B:\angle C=3:4,$ then $\angle B$ = ____ and $\angle C$ = ____.

1. $\angle B={12}^{\circ },\angle C={72}^{\circ }$
2. $\angle B={36}^{\circ },\angle C={48}^{\circ }$
3. $\angle B={75}^{\circ },\angle C={90}^{\circ }$
4. $\angle B={33}^{\circ },\angle C={44}^{\circ }$

Q. One of the interior opposite angles of a triangle is ${40}^o$. If the measure of the exterior angle is ${120}^o$, find the measure of the other two angles of the triangle.

Q. Using the exterior angle property, find the value of $y$ from the figure.

1. ${100}^{\circ }$
2. ${20}^{\circ }$
3. ${80}^{\circ }$
4. ${50}^{\circ }$

Q. Answer the questions with reference to the adjoining figure.



(1) Which triangles include points M and N?

(2) Which triangles have point E on their exterior?

(3) Which triangles have seg PS as a common side?

(4) Name the triangles in which ∠PTR is an exterior angle.

(5) Which triangles include points E, M and N?

(6) Of which triangles does ∠PSQ from an exterior angle?

(7) Which points in the figure are in the exterior of all triangles?

(8) Which points are outside ∆PQS but inside ∆PTR?

(9) Identify and name the exterior angles of ∆PST.

(10) List the triangles of which ∠PQS is an angle.

(11) Of which triangles is R a vertex?

(12) Which points lie outside ∆PST?

Q.

Find x.

1. 44${}^{\circ }$

2. 55${}^{\circ }$

3. 66${}^{\circ }$

4. 77${}^{\circ }$

Q.

In the figure, sides $PQ$ and $RQ$ of $△PQR$ are produced to points $S$ and $T,$ respectively. If $\angle SPR={135}^{\circ }$ and $\angle PQT={110}^{\circ }$, find $2\angle PRQ.$

1. ${90}^{\circ }$

2. ${150}^{\circ }$

3. ${110}^{\circ }$

4. ${130}^{\circ }$

Q.

In the given figure, if $\angle CAD={150}^{\circ }$ and $\angle ABC={60}^{\circ },$ then reflex $\angle ACB=$___ .

1. 1 right angle

2. 2 right angles

3. 3 right angles

4. 4 right angles

Q. The exterior angle of a triangle is ______each of its two opposite interior angles.

1. equal to
2. difference of
3. greater than
4. lesser than

Q. Sum of two opposite interior angles of a triangle is equal to it's angle.

1. exterior
2. interior
3. right