Nevaeh has 12 gallons of gas in her car at the beginning of a trip. Every hour Nevaeh

A triangle ABC is inscribed in a circle, such that AB is a diameter. What are the measures of angles of this triangle if: measur

shutvik [7]

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°

4 0

1 year ago

Emily an her dad share the cost of the meal in the ratio 2:3 emily’s Dad pays £52.20 what is the total cost of the meal

rodikova [14]

£87.00

Emily's dad pays 3 parts of the meal

Divide £52.20 by 3 to find one part of the ratio

$\frac{52.20}{3}$ = £17.40 ← 1 part of the ratio

2 parts = 2 × £17.40 = £34.80 ← Emily's share

total cost = £52.20 + £34.80 = £87.00

6 0

2 years ago

Read 2 more answers

Explain how your work your knowledge of place value helps you divide a number in thousands by whole numbers to 10 give a example

Anna71 [15]

Place value is the value each digit has in its position: in order from higher to lower value, there is thousands, hundreds, tens, and ones.
When you divide by 10, you are moving (only once) every digit from its present place value to the right.
For example 6430 : 10= 643, you have moved every digit to the right, making the zero disappear (or better yet, separated by a hidden and in this case useless comma).

3 0

2 years ago

An arena receives $1,700 per event for 12 concerts. If the costs for this sponsorship total $14,000, what is the profit margin f

Jobisdone [24]

Answer:

The profit margin for the concert sponsorship is 31.3725 %

Step-by-step explanation:

An arena receives for 1 event = $1700

An arena receives for 12 events = $12 \times 1700$