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3 years ago

In the diagram below, O is circumscribed about quadrilateral DEFG. What is the value of x?

Mathematics

1 answer:

Fofino [41]3 years ago

7 0

Answer:

A. 70

Step-by-step explanation:

The given quadrilateral DEFG is a cyclic quadrilateral.

$\angle F+70\degree=180\degree$ ...opposite angles of a cyclic quadrilateral are supplementary.

$\implies \angle F=180\degree-70\degree$

$\implies \angle F=110\degree$

The sum of angles in a quadrilateral is 360 degrees.

$x-10+70+110+120=360$

$x+290=360$

$x=360-290$

$x=70\degree$

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3 years ago

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2 years ago

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In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.

solmaris [256]

Answer:

1. m∠R > 90°

2. m∠S + m∠T < 90°

4. m∠R > m∠T

5. m∠R > m∠S

Step-by-step explanation:

<h3>General strategy</h3>

prove the statement starting from known facts, or
disprove the statement by finding a counterexample

Helpful fact: Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.

Option 1. m∠R > 90°

Start with m∠R > m∠S + m∠T.

Adding m∠R to both sides of the inequality...

m∠R + m∠R > m∠R + m∠S + m∠T

There are two things to note here:

The left side of this inequality is 2*m∠R
The right side of the inequality is exactly equal to the Triangle Sum Theorem expression

2* m∠R > 180°

Dividing both sides of the inequality by 2...

m∠R > 90°

So, the first option must be true.

Option 2. m∠S + m∠T < 90°

Start with m∠R > m∠S + m∠T.

Adding (m∠S + m∠T) to both sides of the inequality...

m∠R + (m∠S + m∠T) > m∠S + m∠T + (m∠S + m∠T)

There are two things to note here:

The left side of this inequality is exactly equal to the Triangle Sum Theorem expression
The right side of the inequality is 2*(m∠S+m∠T)

Substituting

180° > 2* (m∠S+m∠T)

Dividing both sides of the inequality by 2...

90° > m∠S+m∠T

So, the second option must be true.

Option 3. m∠S = m∠T

Not necessarily. While m∠S could equal m∠T, it doesn't have to.

Example 1: m∠S = m∠T = 10°; By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.

Example 2: m∠S = 15°, and m∠T = 10°; By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.

So, option 3 does NOT have to be true.

Option 4. m∠R > m∠T

Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.

Add m∠T to both sides.

(m∠S) + m∠T > (0) + m∠T

m∠S + m∠T > m∠T

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠T.

So, option 4 must be true.

Option 5. m∠R > m∠S

Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.

Add m∠S to both sides.

m∠S + (m∠T) > m∠S + (0)

m∠S + m∠T > m∠S

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠S.

So, option 5 must be true.

Option 6. m∠S > m∠T

Not necessarily. While m∠S could be greater than m∠T, it doesn't have to be. (See examples 1 and 2 from option 3.)

So, option 6 does NOT have to be true.

4 0

1 year ago

3 lines are shown. A line with points C, A, F intersects a line with points E, A, B at point A. A line extends from point A to p

Verizon [17]

Answer:

m < EAD = 29 degrees

m < CAB = 119 degrees

Given :

The question states that m < CAE = m<FAB = 61 degrees and m<DAF = 90 degrees

Solution:

1. Since line CAF and EAB intersect each other, m<CAF = m< EAF - (opposite vertical angles are equivalent)

2. m<BAC + m<EAC = 180 degrees (sum of linear pair)

3. m<CAB = 180 degrees - m<EAC

4. Equation 1: m<CAB = m<EAF = 119 degrees

5. m<EAF = m<EAD + m< DAF

6. m<EAD = m<EAF - m<DAF

7. m<EAD = 119 degrees-90 degrees = 29 degrees

Hope this helps!!! :)

Attached photo work is created by another brainly user named tallinn.

Click on this link to find his work and possibly more information of the answer. Thanks!

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3 years ago

Andrew uses 630 one-inch unit cubes to completely fill the inside of a rectangular box. Which could be the dimensions of the box

dsp73

we have 630 one-inch unit cubes and we want to completely fill the rectangular box (unknown dimensions).

If all the cubes are fitted tightly inside rectangular box without living any space, then box volume would be equal to cubes volume.

There are 630 one-inch unit cubes, so volume of cubes = 630 cubic inches.

Now the volume of rectangular box would also be 630 cubic inches.

We know the formula for volume of rectangular box = length × width × height.

So we need to find any three positive integers whose product is 630.

Out of all given choices, only option A satisfies the condition of factors of 630.

Hence, option A i.e. (7 in x 9 in x 10 in) is the final answer.

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3 years ago