Question

In triangle ABC,angle B is three times larger as angle A. Angle C measures 5 degree more than angle B. Find the measure of each angle.​

Answer 1

Step-by-step explanation:

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Answer 2

$\bf{\huge{\underline{\boxed{\rm{\pink{Answer:}}}}}}$

Given:-

In Δ ABC,

• angle B is three times larger as angle A
• Angle C measures 5 degree more than angle B

To find :-

• the measure of each angle.

Solution :-

Let angle A = x

Let angle B = 3x

Let angle C = 3x + 5

We know that, the sum of all the angles of a triangle is 180°, therefore using this property of triangle we will work out the question.

x + 3x + 3x + 5 = 180

x + 6x + 5 = 180

7x + 5 = 180

7x = 180 - 5

7x = 175

x = $\bf\large\frac{175}{25}$

x = 25

Substitute the value of x in the values of angles to find the measure of each angle of the triangle.

$\bf{\large{\underline{\boxed{\rm{\red{<strong><u> </u></strong><strong><u>Angle </u></strong><strong><u>A </u></strong><strong><u>=</u></strong><strong><u> </u></strong><strong><u>x </u></strong><strong><u>=</u></strong><strong><u> </u></strong><strong><u>25°</u></strong>}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\blue{ <strong><u>Angle </u></strong><strong><u>B </u></strong><strong><u>=</u></strong><strong><u> </u></strong><strong><u>3x </u></strong><strong><u>=</u></strong><strong><u> </u></strong><strong><u>3 </u></strong><strong><u>×</u></strong><strong><u> </u></strong><strong><u>25 </u></strong><strong><u>=</u></strong><strong><u> </u></strong><strong><u>75°</u></strong>}}}}}}$

$\bf{\large{\underline{\boxed{\rm{\pink{Angle\:C\:=\:3x + 5 = 3 × 25 + 5 = 75 + 5 = 80°}}}}}}$

$\bf{\huge{\underline{\boxed{\rm{\orange{Verification:}}}}}}$

• Measure of Angle A = 25°
• Measure of Angle B = 75°
• Measure of Angle C = 80°

Sum of measures of all angles of a triangle = 180°

Angle A + Angle B + Angle C = 180°

25 + 75 + 80 = 180

100 + 80 = 180

180 = 180

LHS = RHS.

Hence verified!