Lines and Angles Test - 19

Let the required angle be $$x$$, then its supplement $$=(180-x)\quad $$ 

Let's try and prove the exterior angle property for a triangle.

For the given triangle $$XZY$$,

$$\angle 1+\angle 2+\angle XZY=180^{o}$$

Also, $$\angle 3+\angle XZY=180^{o}$$ ......... (Linear pair of angles)

$$\angle 1+\angle 2+\angle XZY=\angle 3 +\angle XZY$$

$$\Rightarrow \angle 3=\angle 1+\angle 2$$ ...... (which is the Exterior angle property).

Therefore, we can say that an exterior angle of a triangle is equal to the sum of the two interior opposite angles.
That is, the statement is true.

Hence, option $$A$$ is correct.

Consider the given triangle, we can easily apply exterior angle property of triangle.

For given triangle $$XYZ$$,

$$\angle 1+\angle 2+\angle z=180^{o}$$

Also, $$\angle 3+\angle z=180^{o}$$ ......... (Linear pair of angles)

$$\angle 1+\angle 2+\angle z=\angle 3 +\angle z$$

$$\Rightarrow \angle 3=\angle 1+\angle 2$$ ...... (which is the Exterior angle property).

Therefore, we can say that, an exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Hence, option $$A$$ is correct.

We know, two angles whose sum is equal to $$90^o$$ are known as complementary angles.

Also, acute angle is the angle which is greater than $$\displaystyle { 0 }^{ o }$$ and less than $$\displaystyle { 90 }^{ o }$$.

Hence, iftwo angles are complement of each other, then each of them should necessarily be acute angle.

Therefore, option $$C$$ is correct.

We know that linear pair of angles are supplementary i.e., they add up to form $$180^\circ$$

If a ray stands on a line, then the sum of two adjacent angles so formed is equal to $$180^\circ$$ which is also known as a linear pair.

Let the required angle be $$ x$$.

$$Two\quad angles\quad are\quad supplementary\quad when\quad they\quad add\quad upto\quad form\quad 180\quad degrees\quad .\\ If\quad one\quad angle\quad =\quad 54\\ Let\quad the\quad other\quad angle\quad be\quad x\\ Hence\quad x\quad =\quad 180-54\\ =126\\ Hence\quad supplementary\quad angle\quad of\quad the\quad following\quad angle\quad is\quad 126$$

Let one angle be $$\angle x$$
$$\therefore$$ other angle is $$\angle x+25^o$$
Now,
   We know, by angle sum property, the sum of all angles of a triangles is $$ 180^0$$.
$$\implies x+x+25^o+65^o=180^o$$
$$\implies 2x=180^o-90^o$$
$$\implies x=45^o$$
Thus, the angles are $$45^o$$ and $$70^o$$

Two angles are supplementary when they add upto form $$180^o$$.