Question

18. If ZW and ZV are supplementary angles and m2V = 49°, find m/W.

19. If 21 and 22 are vertical angles, <2 and <3 are complementary angles,
and m23 = 56°, find m21.

Answer 1

Explanation:

18. Supplementary angles add up to 180°therefore

∠W+∠V=180°

∠W+49°=180°

∠W=180°-49°

∠W=131°

19.Complementary angles are angles that add up to 360°

∠2+∠3=90°

∠2+56°=90°

∠2=90°-56°

∠2=34°

Vertical angles are equal therefore this tells us that ∠1 and ∠2 are equal

∠1=∠2

∴∠1=34°

20. Angles which are in a linear pair add up to 180°(supplementary)

Mathematically what the statement is sayin is :

∠1+∠2=180°

and ∠1=5(∠2)-18°

therefore we can plug in ∠1=5(∠2)-18° in ∠1+∠2=180°

(5(∠2)-18°)+∠2=180°

5(∠2)+∠2=180°+18°

6(∠2)=192°

`(6 < 2)/(6) =(198)/(6) \\ < 2=33`

∠1=5(33°)-18°

∠1=165°-18°

∠1=147°