Answer:
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°
