Question

one of the angles of the triangle is equal to the sum of the other 2 angles. if the ratio of the other 2 angles is 4:5, find measures of all angles
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Answer 1

Answer :

›»› The measure of all angles of a triangle is 40°, 50°, and 90° respectively.

Given :

• One of the angles of the triangle is equal to the sum of the other 2 angles.
• The ratio of the other 2 angles is 4:5.

To Find :

• The measure of all angles of a triangle.

Solution :

Let us assume that, the measure of two angles is 4x and 5x respectively.

As it is given that, one of the angles of the triangle is equal to the sum of the other 2 angles.

→ 1st angle + 2nd angle = 3rd angle.

→ 4x + 5x = 9x

The angles of a triangle is 4x, 5x, 9x respectively.

As we know that

The sum of all three angles of a triangle is 180°.

→ 4x + 5x + 9x = 180

→ 9x + 9x = 180

→ 18x = 180

→ x = 180/18

→ x = 10

Therefore,

• 4x = 4 * 10 = 40°.
• 5x = 5 * 10 = 50°.
• 9x = 9 * 10 = 90°.

Hence, the measure of all angles of a triangle is 40°, 50°, and 90° respectively.

Verification :

The sum of all three angles of a triangle is 180°.

→ 40 + 50 + 90 = 180

→ 90 + 90 = 180

→ 180 = 180

Here, LHS = RHS

Hence Verified !

Answer 2

Answer:

$\huge \bf \maltese \: solution \maltese$

$\small \tt \underline {firstly \: lets \: understand \: the \: concept}$

There is a triangle in which two sides are given in ratio 4:5. We have to find measure of all angle. So, for this we have to find the third angle.

Let the sides be 4x and 5x

As we know sum of two sides = third sides

$\sf \: 4x + 5x = 9x$

Now,

As we are knowing that sum of all sides of triangle is 180⁰.

Then,

$\sf \implies4x + 5x + 9x = 180 \degree$

$\sf \implies \: 18x = 180 \degree$

$\sf \implies \: x \: = \frac{180}{18}$

$\sf \implies \: x \: = 10$

Therefore,

Angle will be

4x = 4(10) = 40⁰

5x = 5(10) = 50⁰

9x = 9(10) = 90⁰

$\small \tt \underline {dont \: be \: confused \: lets \: verify \: it}$

$\sf \implies \: 40 + 50 + 90 = 180$

$\sf \implies \: 90 + 90 = 180$

$\sf \implies \: 180 = 180$

$\sf\:lhs \: = rhs$

Hence verified