40, 100 and 83, 143.
74, 164 36, 126 18, 108
The measure of an angle formed by two intersecting chords in a circle is equal to half the sum of the measures of the intercepted arcs. This means that if two arcs, ( A ) and ( B ), are intercepted by the angle, the angle's measure can be calculated using the formula: ( \text{Angle} = \frac{1}{2} (mA + mB) ), where ( mA ) and ( mB ) are the measures of the intercepted arcs. This relationship helps in solving various problems involving angles and arcs in circle geometry.
true
150
True. The measure of a tangent-tangent angle is indeed half the difference of the measures of the intercepted arcs. This theorem applies to angles formed outside a circle by two tangents that intersect at a point, providing a relationship between the angle and the arcs it intercepts.
56, 126,40, 110,and 77, 147.
It is the measure of half the intercepted arc.
74, 164 36, 126 18, 108
Examples to show how to use the property that the measure of a central angle is equal to the measure of its intercepted arc to find the missing measures of arcs and angles in given figures.
True
The measure of an angle formed by two intersecting chords in a circle is equal to half the sum of the measures of the intercepted arcs. This means that if two arcs, ( A ) and ( B ), are intercepted by the angle, the angle's measure can be calculated using the formula: ( \text{Angle} = \frac{1}{2} (mA + mB) ), where ( mA ) and ( mB ) are the measures of the intercepted arcs. This relationship helps in solving various problems involving angles and arcs in circle geometry.
true
150
The answer is half the measure, 62°. Have a nice day!
True. The measure of a tangent-tangent angle is indeed half the difference of the measures of the intercepted arcs. This theorem applies to angles formed outside a circle by two tangents that intersect at a point, providing a relationship between the angle and the arcs it intercepts.
When two segments intersect outside a circle, the measure of the angle formed by the intersecting segments is equal to half the difference of the measures of the intercepted arcs. Specifically, if the angle is formed by segments that intersect outside the circle, the angle's measure is calculated as (Arc 1 - Arc 2)/2, where Arc 1 and Arc 2 are the measures of the arcs intercepted by the angle on the circle. This relationship helps in solving various geometric problems involving circles and angles.
4/9*pi*r where r is the radius of the circle.