Mathematics, 30.07.2019 05:00 yourmumsanoodle

Quadrilateral abcd is inscribed in this circle. what is the measure of angle c? enter your answer in the box

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1. The sum of the opposite angles of the quadrilateral ABCD that is inscribed in the circle, is 180°. Therefore, the sum of all the angles is 360°.

2. As you can see, m∠B=(2x-1)° and m∠D=(3x-59)° are opposite angles, then:

m∠B+m∠D=180°

3. When you substitute the values of m∠B and m∠D into m∠B+m∠D=180°, you obtain:

m∠B+m∠D=180°
(2x-1)+(3x-59)=180°

4. You must clear the "x", as below:

(2x-1)+(3x-59)=180°
5x-60=180
x=48°

5. Now, you can find the value of m∠A, m∠B and m∠D:

m∠A=2x+4
m∠A=2(48)+4
m∠A=100°

m∠B=2x-1
m∠B=2(48)-1
m∠B=95°

m∠D=3x-59
m∠D=3(48)-59
m∠D=85°

6. Therefore, the value of m∠C is:

m∠A+m∠B+m∠C+m∠D=360°
m∠C=360-m∠A-m∠B-m∠D
m∠C=360°-100°-95°-85°
m∠C=80°

What is the measure of angle C?

The answer is: 80°

Answer from: Quest

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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Quadrilateral abcd is inscribed in this circle. what is the measure of angle c? enter your answer...