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3 years ago

The three angles of a triangle have measures

Mathematics

1 answer:

slava [35]3 years ago

6 0

The correct answer is: B. 47 degrees

Step-by-step explanation:

Given

Let A,B and C be the three angles

∠A = 8x+6

∠B = 7x-8

∠C = 5x+2

As we know that sum of angles of a triangle is 180°

Mathematically

∠A+∠B+∠C=180°

(8x+6)+(7x-8)+(5x+2) = 180°

8x+6+7x-8+5x+2=180°

20x=180°

dividing both sides by 20

20x/20 = 180/20

x= 9

The angles will be:

∠A = 8x + 6 = 8(9)+6 = 72+6 =78°

∠B = 7x-8 = 7(9)-8 = 63-8 = 55°

∠C = 5x+2 = 5(9) +2 = 47°

The smallest angle is 47°

Hence,

The correct answer is: B. 47 degrees

Keywords: Triangle, Angles

Learn more about triangles at:

#LearnwithBrainly

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6. Find QR, if area and altitude PS of ∆PQR are given<br> ar(∆PQR) = 180 cm2, PS = 15

Slav-nsk [51]

Given:

Area and altitude PS of ∆PQR are ar(∆PQR) = 180cm² and PS = 15.

To find:

The measure of side QR.

Solution:

According to the given information, PS is an altitude of ∆PQR. It means QR is the base of ∆PQR.

We know that, the area of a triangle is

$Area=\dfrac{1}{2}\times Base\times Height$

$ar(\Delta PQR)=\dfrac{1}{2}\times QR\times PS$

Substituting the given values, we get

$180=\dfrac{1}{2}\times QR\times 15$

$180\times 2=QR\times 15$

$360=QR\times 15$

Divide both sides by 15.

$\dfrac{360}{15}=QR$

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Therefore, the measure of side QR is 24 cm.

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nlexa [21]

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