Question

Circle U is shown. Chords R T and Q S intersect at a point forming 4 angles. The top left angle is angle 1, and the top right angle is angle 2. Arc R Q is 53 degrees and arc S T is 47 degrees. Angle 1 intersepts arc R Q. Angle 2 intersepts arc R S.
What are the measures of angles 1 and 2?

m∠1 =

°

m∠2 =
°

Answer 1

Answer:

• ∠1 = 50°
• ∠2 = 130°

Step-by-step explanation:

The relation between intercepted arcs and angles at crossing chords can be used to find the angles of interest. That relation tells you the angle where the chords cross is half the sum of the intercepted arcs.

Angle 1

The arcs intercepted by the chords making angle 1 are given as 53° and 47°. Half their sum is the measure of angle 1:

  ∠1 = (53° +47°)/2 = 100°/2

  ∠1 = 50°

Angle 2

Angles 1 and 2 form a linear pair, so angle 2 is the supplement of angle 1.

  ∠2 = 180° -∠1 = 180° -50°

  ∠2 = 130°

Answer 2

Based on the calculations, the measures of angles 1 and 2 are 50° and 135° respectively.

What is the theorem of intersecting chord?

The theorem of intersecting chord states that when two (2) chords intersect inside a circle, the measure of the angle formed by these chords is equal to one-half (½) of the sum of the two (2) arcs it intercepts.

By applying the theorem of intersecting chord to circle U shown in the image attached below, we can infer and logically deduce that angle 1 will be given by this formula:

m∠1 = ½(53 + 47)

m∠1 = ½(100)

m∠1 = 50°.

Since angles 1 and 2 are linear pair, they are supplementary angles. Thus, we have:

m∠1 + m∠2 = 180°

m∠2 = 180 - m∠1

m∠2 = 180 - 50

m∠2 = 130°.

Read more on intersecting chords here: brainly.com/question/27251228

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