Question

If one of the angles of a triangle is 65º and the other two angles are in the ratio of 2 : 3 .Find
the other two angles.
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Answer 1

Answer:

${\bold{\therefore B=46\degree}}$

${\bold{\therefore C=69\degree}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about a triangle whose one angle is given and ratio between other two angles are given.

• Let ABC be the triangle

• We have to find the other two angles.

$\underline \bold{Given : } \\ \bold{Let \: ABC\: is \: a \: triangle} \\ \implies \angle A = 65 \degree \\ \implies ratio = 2 : 3 \\ \implies let \: \angle B = 2x \\ \implies \: \: \: \: \: \angle C = 3x \\ \\ \underline \bold{To \: Find : } \\ \implies \angle B = ? \\ \implies \angle C= ?$

• According to given question :

$\bold{ By \:triangle\:property}\\ \implies \angle A+ \angle B+ \angle C = 180 \degree \\ \implies 65 \degree + 2x + 3x = 180 \degree \\ \implies 5x = 180 \degree - 65 \degree \\ \implies 5x = 115 \degree \\ \implies x = \frac{115 \degree}{5} \\ \bold{\implies x = 23 \degree} \\ \\ \implies \angle B = 2x = 2 \times 23 \\ \bold{\therefore \angle B = 46 \degree} \\ \\ \implies \angle C = 3x = 3 \times 23 \\ \bold {\therefore \angle C= 69 \degree}$