Atriangle abc is inscribed in a circle, such that ab is a diameter. what are the measures of angles of this triangle if: measure of arc bc = 134°;

The measures of angles of this Δ are 23° , 67° , 90°

Step-by-step explanation:

* Lets talk about some facts in the circle

- An inscribed angle is an angle made from points sitting on the

 circle's circumference

- A central angle is the angle formed when the vertex is at the center

 of the circle

- The measure of an arc of a circle is equal to the measure of the

 central angle that intercepts the arc.

- The measure of an inscribed angle is equal to 1/2 the measure of

 its intercepted arc

- An angle inscribed across a circle's diameter is always a right angle

- The triangle is inscribed in a circle if their vertices lie on the

  circumference of the circle, and their angles will be inscribed

  angles in the circle

* Now lets solve the problem

- Δ ABC is inscribed in a circle

∵ its side AB is a diameter of the circle

∵ Its vertex C is on the circle

∴ ∠C is inscribed and across the circle's diameter

∴ ∠C is a right angle

∴ m∠C = 90°

∵ The measure of arc BC = 134°

∵ ∠A is inscribed angle subtended by arc BC

∵ The measure of an inscribed angle is equal to 1/2 the measure

   of its intercepted arc

∴ m∠A = 1/2 × 134° = 67°

∵ The sum of the measures of the interior angles of a triangle is 180°

∵ m∠A = 67°

∵ m∠C = 67°

∵ m∠A + m∠B + m∠C = 180°

∴ 67° + m∠B + 90° = 180°

∴ 157° + m∠B = 180° ⇒ subtract 157 from both sides

∴ m∠B = 23°

* The measures of angles of this Δ are 23° , 67° , 90°

|-23|, |29|, |34|, |-38|, |-45|, |-47|, |-59|,   |67|, |-78|, |-110|, |-514|, |710|

step-by-step explanation:

absolute value gets rid of any negative

1. for division, flip the second fraction.

2. factor the numerator and denominator completely.

3. divide out common factors.

4. multiply the simplified fractions.