Answer:
16. [tex]x = 80^\circ[/tex]
17. [tex]x = 55, y =70, z = 55[/tex]
18. [tex]x =8, y =3[/tex]
19. [tex]r = 66^\circ[/tex], [tex]t = 73^\circ[/tex]
20. [tex]y = 70^\circ, x = 55^\circ[/tex]
21. [tex]x =56^\circ, y = 62^\circ[/tex]
Step-by-step explanation:
16. Side [tex]AB = AC[/tex]
So, the opposite angles of the triangle will also be equal.
[tex]\angle B =\angle C = 50^\circ[/tex]
Using triangle sum property, angle of all the internal angles of a triangle is equal to [tex]180^\circ[/tex].
[tex]50+50+x = 180\\\Rightarrow x = \bold{80^\circ}[/tex]
17. Two sides are given as equal, [tex]x = z[/tex]
Angles on a straight line are always equal to [tex]180^\circ[/tex].
So,
[tex]x + 125 = 180\\\Rightarrow x = 55[/tex]
[tex]z = 55[/tex]
Using triangle sum property, angle of all the internal angles of a triangle is equal to [tex]180^\circ[/tex].
[tex]55+55+y = 180\\\Rightarrow y = \bold{70^\circ}[/tex]
18. All the angles are given equal to each other, therefore all the sides of the triangle will also be equal to each other.
[tex]4x+7 = 13y =39[/tex]
[tex]13y = 39\\\Rightarrow y = 3[/tex]
[tex]4x +7 = 39\\\Rightarrow 4x = 32\\\Rightarrow x = 8[/tex]
19. Two sides are given equal to each other, therefore angles opposite to them will be equal.
Using the triangle sum property in the left triangle:
[tex]r + 57 + 57 = 180\\\Rightarrow r = 66^\circ[/tex]
Using the property that vertically opposite angles are equal and the triangle sum property in the right triangle.
[tex]t+50+57 = 180 \\\Rightarrow t = 73^\circ[/tex]
20. All the sides are given equal to each other.
So, all the angles will be equal to [tex]60^\circ[/tex].
[tex]y - 10 = 60\\\Rightarrow y = 70^\circ[/tex]
[tex]x+5=60\\\Rightarrow x = 55^\circ[/tex]
21. Angles on a straight line are always equal to [tex]180^\circ[/tex].
Angles opposite to equal sides in a triangle are also equal.
[tex]118 + y = 180\\\Rightarrow y = 62^\circ[/tex]
Using triangle sum property:
[tex]x+2y = 180\\\Rightarrow x = 180 - 124 = \bold{56^\circ}[/tex]
