Exterior Angle of a Triangle = Sum of Opposite Internal Angles

Write a relation between the exterior angle of a triangle with interior opposite angles

If two interior opposite angles of a triangle are equal and the external angle is given to be $110°,$then each of the equal interior angles is ____.

Question 24

For the given figure statements p and q are given below:
p: a and b are forming a linear pair.
q: a and b are forming a pair of adjacent angles.
Then,

(a) both p and q are true
(b) p is true and q is false
(c) p is false and q is true
(d) both p and q are false

If an angle measuring 60${}^{\circ }$ is divided in the ratio of 1:3, then the bigger angle will measure ___.

1. 25${}^{\circ }$

2. 45${}^{\circ }$

3. 75${}^{\circ }$

4. 30${}^{\circ }$

1. $37\frac{1^0}{2}$
2. $72\frac{1^0}{2}$
3. $52\frac{1^0}{2}$
4. ${75}^0$

1. $a={55}^{\circ },b={125}^{\circ }$
   $c={55}^{\circ },d={125}^{\circ },e={55}^{\circ },f={55}^{\circ }$
2. $a={45}^{\circ },b={130}^{\circ }$
   $c={55}^{\circ },d={135}^{\circ },e={55}^{\circ },f={50}^{\circ }$
3. $a={55}^{\circ },b={225}^{\circ }$
   $c={45}^{\circ },d={25}^{\circ },e={65}^{\circ },f={55}^{\circ }$
4. $a={35}^{\circ },b={25}^{\circ }$
   $c={75}^{\circ },d={225}^{\circ },e={50}^{\circ },f={60}^{\circ }$

1. $\angle A+\angle C$
2. $\angle B+\angle C$
3. $\angle A+\angle B$

1. ${85}^o$
2. ${65}^o$
3. ${45}^o$
4. ${35}^o$

1. ${90}^o$
2. ${120}^o$
3. ${100}^o$
4. ${110}^o$

Question 1 (iii)
Find the value of the unknown exterior angle x in the following diagrams:

1. ${60}^{\circ }$
2. ${66}^{\circ }$
3. ${55}^{\circ }$
4. ${80}^{\circ }$

1. $x+z=a+b$
2. $y+z=a+b$
3. $m+x=w+n$
4. $x+y+n=a+b+m$