Question

The three inside angles ( A, B and C) of a right-angled triangle
are in the ratio 7 : 18 : 11

The smallest angle is 35° .

Work out angles A, B and C

Answer 1

Step-by-step explanation:

Let the common multiplier of the given ratios be x.

Therefore, measures of angles will be 7x, 18x and 11x.

It is given that: Smallest angle is 35° .

$\therefore \: 7x = 35 \degree \\ \\ \therefore \: x = \frac{35 \degree}{7} \\ \\ \therefore \: x = 5 \degree \\ \\ \implies \\ \: 7x = 7 \times 5 \degree = 35 \degree \\ \: 18x = 18 \times 5 \degree = 90 \degree \\ \: 11x = 11\times 5 \degree = 55 \degree$

Answer 2

The measure of angles in ΔΔABC are

∠ A = 35° , ∠B =90° and  ∠C = 55°

Explanation:

Given : The three inside angles ( A, B and C) of a right-angled triangle  are in the ratio 7 : 18 : 11

Let the angles are 7x , 8x and 11x.

Since the measure of the smallest angle is 35° .

Then,

$7x=35^{\circ}\\\\ x=\dfrac{35^{\circ}}{7}=5^{\circ}$

Then, the measure of other angles will be :

$18x= 18(5^{\circ})=90 ^{\circ}$

$11x=11(5^{\circ}) =55^{\circ}$

Hence, The measure of angles in ΔΔABC are

∠ A = 35° , ∠B =90° and  ∠C = 55°

# Learn more :

In triangle ABC, angke A -angle B =63 degrees, angle B -angle C = 18 degrees, find the measure of angle B

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