Question

A quadrilateral is inscribed in circle O. The angle measures of the quadrilateral, in degrees, are given by the expressions shown in the figure. The diagram shows an inscribed quadrilateral ABCD with the midpoint O, in which angle A 130 minus x, angle B 4x plus 35, angle C 95 minus 2x, and angle D 7x minus 20.

Answer 1

∠ABO is 88°. therefore, option 2. 88° is correct.

To find the measure of angle ∠ABO in the quadrilateral ABCD inscribed in a circle with center O, we can use the property that the opposite angles in an inscribed quadrilateral are supplementary.

In this case, ∠BOC is opposite to ∠AOD, and ∠ADC is opposite to ∠ABC. Therefore, we have:

∠AOD + ∠ABC = 180°

Given that ∠BOC = 92° and ∠ADC = 112°, we can substitute these values into the equation:

92° + ∠ABC = 180°

Now, solve for ∠ABC:

∠ABC = 180° - 92°

∠ABC = 88°

Now, ∠ABC is also opposite to ∠ABO. So,

∠ABO = ∠ABC = 88°

Therefore, ∠ABO is 88°. therefore, option 2. 88° is correct.

Question

A quadrilateral ABCD is inscribed in circle with center o. if ∠BOC =92° and ∠ADC =112° then ∠ABO is equal to:

1. 22°

2. 88°

3. 76°

4. 54°