CIRCLES C7

In the figure below, find the value of <RUS.

Solution

<RSU = <TRU

∴ <RSU = 54⁰ [angles in alternate segments are equal.]

Consider ∆SRU

<SRU + <RUS+ <RSU = 180⁰ [total degrees of a triangle]

 (46⁰ + 54⁰) + <RUS + 54= 180⁰

100⁰ + <RUS + 54⁰ = 180⁰

154⁰ + <RUS= 180⁰

<RUS= 180⁰ - 154⁰

<RUS= 26⁰  

∴ <RUS = 26⁰