1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dmitrij [34]
2 years ago
15

Given: △ABC, Bisectors of ∠A and ∠B meet at O Prove: m∠AOB>90°

Mathematics
1 answer:
Naya [18.7K]2 years ago
3 0

Answer:

The proof is given below.

Step-by-step explanation:

Let the measure of angle A be 2x and B be 2y.

Now, from the triangle ΔABC,

m\angle A+m\angle B+m\angle C=180\\2x+2y+m\angle C = 180\\2(x+y)=180-m\angle C

As angle C is a positive quantity, so, 2(x+y) will be less than 180.

Therefore, 2(x+y)....... 1

Now, for triangle ΔAOB,

Since AO is an angle bisector of m\angle A, therefore, m\angle OAB = \frac{2x}{2}=x

Similarly, m\angle ABO = \frac{2y}{2}=y

Now, sum of all the interior angles of a triangle is 180 degrees.

∴ m\angle AOB + m\angle ABO + m\angle OAB=180

m\angle AOB +y+x=180\\m\angle AOB =180-(x+y)

Now, consider the inequality 1.

x+y

Multiplying by -1 on both sides. This changes the sign of the inequality.

-(x+y)>-90

Adding 180 on both sides, we get

180-(x+y)>180-90\\180-(x+y)>90

But, 180-(x+y)=m\angle AOB

Therefore, m\angle AOB>90. Hence, it is proved.

You might be interested in
What is the value of the expression below?<br> 72 ÷ 4.5x3+8
Fofino [41]

Answer:

56

Step-by-step explanation:

Apply PEMDAS:

72 / 4.5*3+8\\\\16*3+8\\\\48+8\\\\\boxed{56}

4 0
3 years ago
Why is 3/8 bigger than 3/12​
Stolb23 [73]

Answer:

3/ 8  is greater than  3/ 12 because if you cross multiply 12 times 3 is 36 and 3 times 8 is 24

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
The value of a piece of land is $500 an acre. The price per acre is expected to increase 7% per year. Which function models the
kobusy [5.1K]
To set the equation,we can first find how much price would be raised within a year:

=500×(1+7%)

=500×1.07

As the years go by the increase would accumulate,and the equation would be:

500 \times  {1.07}^{t}
Hope it helps!
4 0
3 years ago
PLEASE HELP MEEE
STALIN [3.7K]
If there are 16 ounces in a pound, and 8 ounces costs $8, The best answer would be D. $16 per pound
4 0
3 years ago
Addison earn $25 mowing her neighbor's lawn then she loaned her friend $18 and got 50 from her grandmother for her birthday she
yarga [219]

Solution: The total money did addison have to begin with is $29.

Explanation:

Let the addison begin with money $x.

It is given that the addison earn $25 from his neighbor and $50 from her grandmother. So total money addison has \$x+\$25+\$50=\$x+\$75

She loaned her friend %18.

Now she has \$x+\$75-\$18=\$x+\$57

It is given that she had $86.

\$x+\$57=\$86\\\$x=\$86-\$57\\\$x=\$29

Therefore, the total money did addison have to begin with is $29.

4 0
3 years ago
Read 2 more answers
Other questions:
  • Jill converted the equation of the line 15 x minus 14 y = negative 2 into slope-intercept form and found the slope and y-interce
    15·2 answers
  • jan, mya, and Sara ran a total of 64 miles last week. jan and mya ran the same number of miles. Sara ran 8 less miles than mya.
    7·2 answers
  • Here are the two arguments you will be debating: Argument A: There is a need for students to understand and be able to construct
    7·1 answer
  • What is the property of (20×18) × 5
    9·2 answers
  • Is a Unit rate the same thing as a Proportion?
    8·1 answer
  • What is the median of the data set? <br><br><br>17, 40, 23, 44, 44, 30 <br>​
    12·2 answers
  • 6. Ray Rodriguez will be eligible for retirement benefits in 72 months. How many years remain before Ray
    11·1 answer
  • Factor -4 + 8a - 4a^2
    10·2 answers
  • In a family 3 adults and 2 children visit a play park for a total cost of $1100 and 2 adults and 3 children from another family
    7·1 answer
  • Round 369 962 to the nearest hundred.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!