Answer:
• [tex]x[/tex] = 42°
• [tex]y[/tex] = 74°
• [tex]z[/tex] = 114°
Step-by-step explanation:
To solve these problems, we have to use the triangle sum theorem, which states that "the sum of all the interior angles of a triangle is 180°".
A)
[tex]x[/tex] + 90° + 48° = 180°
⇒ [tex]x[/tex] + 138° = 180°
⇒ [tex]x[/tex] + 138° - 138° = 180° - 138° [Subtracting 138° from both sides]
⇒ [tex]x[/tex] = 42°
B)
The triangle in this question is an isosceles triangle, therefore the two angles at the base of the triangle are equal and have measures of [tex]y[/tex].
[tex]y[/tex] + [tex]y[/tex] + 32° = 180°
⇒ 2[tex]y[/tex] + 32° = 180°
⇒ 2[tex]y[/tex] = 180° - 32°
⇒ 2[tex]y[/tex] = 148°
⇒ [tex]\frac{2}{2} y[/tex] = [tex]\frac{148^{\circ}}{2}[/tex] [Dividing both sides by 2]
⇒ [tex]y[/tex] = 74°
C)
[tex]z[/tex] + 28° + 38° = 180°
⇒ [tex]z[/tex] + 66 = 180°
⇒ [tex]z[/tex] = 180° - 66°
⇒ [tex]z[/tex] = 114°
