Answer:
Question 1. Option (3) RT = 35°
Question 2. Option (3) y = 2
Step-by-step explanation:
By the definition of external angle, ∠PSY is the external angle formed by the secants PS and YS.
From the attached diagram.
Theorem says,
m(∠a) = [tex]\frac{1}{2}(\frac{y-x}{2})[/tex]°
Now we will apply this theorem in our question.
m(∠PSY) = 180° - [m(∠SMX) + m(∠MXS)]
= 180° - (95° + 45°)
= 180° - 140°
= 40°
Since m(∠PSY) = [tex]\frac{1}{2}[m(arcPY)-m(arcRT)][/tex] [By the theorem]
m(arc PY) = m(arc PW) + m(arc WY)
= (80 + 35)°
= 115°
Now m(∠PSY) = [tex]\frac{1}{2}[115-RT][/tex]
40° = [tex]\frac{1}{2}(115-RT)[/tex]°
80 = 115 - RT
RT = 115 - 80
RT = 35°
Therefore, Option (3). RT = 35° is the answer.
Question 2.
By the theorem, every angle at the circumference of a semicircle, that is subtended by the diameter of the semicircle is a right angle.
Therefore, (53y - 16)° = 90°
53y = 90 + 16
53y = 106
y = 2
Therefore, Option (3). y = 2 is the answer.
