Question

Measurement of angle 1

Answer 1

Answer:

55 degrees

Step-by-step explanation:

Given that a circle and inside two chords with same arc length.

We are to find the angle between the two chords.

Given that two arcs subtend angle 125 degrees at the centre.

Let us join the two ends of chords to make the figure as a triangle inside a circle.

The triangle is isosceles as two arcs and hence chords are equal.

By central angle theorem we have the two equal angles as 1/2 (125) = 62.5

Hence we have a triangle with two equal angles 62.5 and another angle 1.

By triangle sum of angles theorem

angle 1+62.5+62.5 = 180

Hence angle A = 180-62.5-62.5 = 55 degrees.