Angles in a triangle

Geometry Level 1

$ABC$ is a triangle such that $\angle CAB = 2 \theta$ , $\angle ABC = 3 \theta$ and $\angle BCA = 5 \theta$ . What is the measure (in degrees) of $\theta$ ?

The answer is 18.

3 solutions

Nelvson Shine
Aug 4, 2013

in a triangle, obviously the sum of degrees is 180, so :

∠CAB + ∠ABC + ∠CBA = 2 $\theta$ + 3 $\theta$ + 5 $\theta$ = 180

10 $\theta$ = 180

$\theta$ = $180 : 10$

$\theta$ = 18

Thus the answer is 18.

Moderator note:

Can you see immediately that this must be a right triangle?

The problem is invalid. ∠ABC and ∠CBA is the same angle based on the law of naming angles in a triangle in which an angle in a triangle can be name by its vertex or by its corresponding vertex in the middle and two more points. point C and point A is two points and point b is the vertex therefore i conclude ∠ABC and ∠CBA are the same angle..

John Clyde Escucha - 7 years, 10 months ago

nope, this is not a right triangle, but i share how i got a correct answer. so that's it.

Nelvson Shine - 7 years, 10 months ago

\angle CAB and \angle CBa are o the same. How can you get the sum of the angles if they are of the same angle. The question is INVALID since theres no such measurement for \angle C to use the sum of the interior angles of the triangle.

Fran Magat - 7 years, 10 months ago

Anna Ruth Alvarez
Aug 6, 2013

2θ + 3θ + 5θ = 180

10θ = 180

θ = 18

Let the angle b X;

Therefore, 2X + 3X + 5X;

SUM OF TOTAL DEGREE OF TRIANGLE IS 180

THEREFORE 2X + 3X + 5X = 180 10X = 180

X = 180/10

X = 18

Laukik Gondalia - 7 years, 10 months ago

Stefanus Arya
Aug 9, 2013

What is 'θ' anyway ? ; but it's a triangle, and it must be 2x + 3x + 5x = 180 (every 2D triangle must be 180 degree) ;10x = 180 ; x = 18... the answer is 18.

Angles in a triangle

The answer is 18.

3 solutions

Moderator note:

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