"Solve for x in the following circles:1)2) 3)" solved and explained - Plainmath

blakkazn924e4y

Answered question

2022-03-03

Solve for x in the following circles:
1)

2) 3)

Answer & Explanation

Miles Martin

Beginner2022-03-04Added 6 answers

Step 1
(1)

∠ A = 360^{\circ} - (100^{\circ} + 70^{\circ} + 150^{\circ}) = 40^{\circ}

By intersecting chord theorem,

x = \frac{1}{2} (40^{\circ} + 100^{\circ}) = 70^{\circ}

(2)

∠ A = 360^{\circ} - (145^{\circ} + 95^{\circ} + 85^{\circ})

= 35^{\circ}

The angleformed by two intersecting secontsis helf of the positive difference of measures of the intercepted ares

x = \frac{1}{2} (145^{\circ} - 35^{\circ}) = 55^{\circ}

(3)

m ∠ A O C + m ∠ A B C = 180^{\circ}

\Rightarrow x = 180^{\circ} - 95^{\circ}

= 85^{\circ}

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