Triangles

1003021701

Level: 
A
Interior angles of a triangle \( ABC \) are in the ratio \( \alpha:\beta:\gamma=2:4:6 \). Calculate the measures of these angles.
\( \alpha=30^{\circ};\ \beta=60^{\circ};\ \gamma=90^{\circ} \)
\( \alpha=20^{\circ};\ \beta=40^{\circ};\ \gamma=60^{\circ} \)
\( \alpha=15^{\circ};\ \beta=30^{\circ};\ \gamma=135^{\circ} \)
\( \alpha=90^{\circ};\ \beta=60^{\circ};\ \gamma=30^{\circ} \)

1003021703

Level: 
A
The measure of an exterior angle of an isosceles triangle is \( 84^{\circ} \). Calculate the measures of all interior angles of the triangle.
\( 96^{\circ};\ 42^{\circ};\ 42^{\circ} \)
\( 84^{\circ};\ 48^{\circ};\ 48^{\circ} \)
\( 12^{\circ};\ 84^{\circ};\ 84^{\circ} \)
\( 96^{\circ};\ 96^{\circ};\ 12^{\circ} \)

1003021705

Level: 
A
Calculate the measures of interior angles \( \alpha \), \( \beta \) and \( \gamma \) of a triangle if \( \gamma=2\beta \) and \( \beta=3\alpha \).
\( \alpha=18^{\circ};\ \beta=54^{\circ};\ \gamma=108^{\circ} \)
\( \alpha=15^{\circ};\ \beta=45^{\circ};\ \gamma=90^{\circ} \)
\( \alpha=12^{\circ};\ \beta=54^{\circ};\ \gamma=111^{\circ} \)
\( \alpha=54^{\circ};\ \beta=18^{\circ};\ \gamma=108^{\circ} \)

1003021707

Level: 
A
Choose the false statement.
All altitudes in a right-angled triangle are perpendicular to one another.
The centroid of a triangle divides each median in the ratio \( 2:1 \).
The midline of a triangle is parallel to the third side and half as long.
The medians of a triangle intersect in a single point, the centroid of a triangle.

1003076801

Level: 
A
\( ABC \) is a triangle with sides \( a \), \( b \), \( c \). Let \( a\leq b\leq c \). Two of its interior angles have measures of \( 70^{\circ} \) and \( 50^{\circ} \). Which of the following statements about the triangle \( ABC \) is true?
The third interior angle is opposite the side \( b \).
The angle of the measure \( 70^{\circ} \) lies opposite the side \( a \).
The angle of the measure \( 50^{\circ} \) lies opposite the side \( b \).
The third interior angle is opposite the side \( c \).