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Novosadov [1.4K]
3 years ago
10

Which statement completes the proof that the sum of the angles of triangle PRQ is 180°? Statement Justification

Mathematics
2 answers:
Nutka1998 [239]3 years ago
8 0

Answer:

The step missing is

m\angle PRQ + m\angle RPQ + m\angle PQR = 180\°, by substitution.

Step-by-step explanation:

We have

\angle 5 \cong \angle PQR by Alternate Interior Angles Theorem.

\angle 1 \cong \angle PRQ, by Alternate Interior Angle Theorem.

m\angle 1 + m\angle RPQ + m\angle 5 =180\°, by Definition of a Straight Angle and a Straight Angle postulate.

\therefore

m\angle PRQ + m\angle RPQ + m\angle PQR = 180\°, by substitution.

Now, remember that Alternate Interior Angles are those which are inside two parallels and different sides of the transversal line which intercept those parallels. Their theorem states that such angles are always congruent.

Then, the definition of a straight angle is that measures 180°, and its postulate is that adjacent angles on an straight angle must sum 180°, and they are supplementary.

vichka [17]3 years ago
7 0
M∠1 + m∠RPQ + m∠5 = 180° Definition of a Straight Angle

proof :  mes1= PRQ (alternate interior)

RPQ = 3 Opposite angle (vertex)
5 =Q  (alternate interior)
PRQ + RPQ + RQP = 180
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HELP PLEASEEE
jeka94

The exact circumference of the circle is 7 \frac{49}{150} k m

The approximate circumference of the circle is 7.33 k m

Explanation:

The diameter of the circle is 2 \frac{1}{3} \mathrm{km}

Now, we shall find the circumference of the circle.

The formula to determine the circumference of the circle is given by

C=\pi d

Where C is the circumference , \pi is 3.14 and d=2 \frac{1}{3} \mathrm is the diameter of the circle.

The exact circumference of the circle is given by

\begin{aligned}C &=\pi d \\&=(3.14)\left(2 \frac{1}{3}\right) \\&=(3.14)\left(\frac{7}{3}\right) \\&=\frac{21.98}{3}\end{aligned}

Multiply both numerator and denominator by 100, we get,

C=\frac{2198}{300} \\C=\frac{1099}{150}

Converting \frac{1099}{150} into mixed fraction, we get,

C=7 \frac{49}{150}

Thus, the exact circumference of the circle is 7 \frac{49}{150} k m

The approximate value of the circumference can be determined by dividing the value \frac{1099}{150}

C=\frac{1099}{150}=7.327

C=7.33km

Thus, the approximate circumference of the circle is 7.33 k m

3 0
3 years ago
Each lenght is in metres Calculate DC​
Gnom [1K]

Step-by-step explanation:

ED is greater than BC

the line from B to ED ^ (which i drew ) the point it touches ED name it X. so EX will be 2 ( ED-BC)(6-4).

then u have a triangle. EX, XB and EB.

you have length of EX(2) and u have hypotenuse. so u can calculate XB using Pythagoras theorem.

15.1²=2²+XB²

15.1²-2²=XB²

224.01=XB²

XB=14.97

since XB and DC are parallel ( a rectangle is forming XBCD) so DC is also 14.97

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Answer:

(0.5,0.5)

Step-by-step explanation:

use the midpoint formula x1+x2/2 and y1+y2/2

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