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4 years ago

Measures of each interior angle

Mathematics

1 answer:

Bogdan [553]4 years ago

4 0

Given:

∠Q = (2x + 5)°, ∠R = x°

∠S = (2x + 7)°, ∠T = x°

To find:

The measure of each interior angle.

Solution:

Sum of all the angles of a quadrilateral = 360°

∠Q + ∠R + ∠S + ∠T = 360°

2x° + 5° + x° + 2x° + 7° + x° = 360°

6x° + 12° = 360°

Subtract 12° from both sides.

6x° = 348°

Divide by 6 on both sides.

x° = 58°

The measure of angle R is 58°.

The measure of angle T is 58°.

Substitute x = 58 in Q, and S.

∠Q = (2(58) + 5)°

= (116 + 5)°

∠Q = 121°

The measure of angle Q is 121°.

∠T = (2(58) + 7)°

= (116 + 7)°

∠T = 123°

The measure of angle T is 123°.

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3 years ago

What is the distance covered by a train while slowing down from

alukav5142 [94]

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The distance covered is 113.75 m

Step-by-step explanation:

As per the question:

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3 years ago

The measure of angle P is five less than four times the measure of angle Q. Of angle P and angle Q are supplementary angles, fin

Andru [333]

Answer:

m∠P=140°

Step-by-step explanation:

Given:

∠P and ∠Q are supplementary angles.

The measure of angle P is five less than four times the measure of angle Q.

To find m∠P

Solution:

The measure of angle P can be given as:

A) $m\angle P=4(m\angle Q-5)$

And

B) $m\angle P+ m\angle Q=180$ [Definition of supplementary angles]

Substituting equation A into B.

$4(m\angle Q-5)+ m\angle Q=180$

Solving for $m\angle Q$

Using distribution:

$4m\angle Q-20+ m\angle Q=180$

Simplifying by combining like terms.

$5m\angle Q-20=180$

Adding 20 to both sides.

$5m\angle Q-20+20=180+20$

$5m\angle Q=200$

Dividing both sides by 5.

$\frac{5m\angle Q}{5}=\frac{200}{5}$

$m\angle Q=40$

Substituting $m\angle Q=40$ in equation B.

$m\angle P+ 40=180$

Subtracting both sides by 40.

$m\angle P+ 40-40=180-40$

$m\angle P=140$

Thus, we have:

m∠P=140° (Answer)

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3 years ago