1003021711
Level:
A
What is the measure of all interior angles in an equilateral triangle?
\( 60^{\circ} \)
\( 30^{\circ} \)
\( 90^{\circ} \)
\( 45^{\circ} \)
Triangles
1003021710
Level:
A
In a right-angled triangle \( ABC \) with a right angle at the vertex \( A \) the measure of the angle \( ABC \) is \( 50^{\circ} \). Give the measure of the angle \( BCA \).
\( 40^{\circ} \)
\( 90^{\circ} \)
\( 30^{\circ} \)
\( 180^{\circ} \)
1103021709
Level:
A
The picture shows an isosceles triangle \( ABC \) with the base \( AB \). Calculate the measure of the angle \( \alpha \).
\( 31^{\circ} \)
\( 62^{\circ} \)
\( 118^{\circ} \)
\( 59^{\circ} \)
1103021708
Level:
A
What is the measure of the angle \( \alpha \)? (See the picture.)
\( 7^{\circ} \)
\( 76^{\circ} \)
\( 83^{\circ} \)
\( 16^{\circ} \)
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.
1103021706
Level:
A
In the triangle \( ABC \), \( \alpha=80^{\circ} \) and \( \beta=70^{\circ} \) (see the picture). Determine the measure of the angle between the altitude to the side \( AB \) and the altitude to the side \( BC \).
\( 70^{\circ} \)
\( 120^{\circ} \)
\( 30^{\circ} \)
\( 60^{\circ} \)
1003021705
Level:
A
Calculate the measures of interior angles \( \alpha \), \( \beta \) and \( \gamma \) of a triangle if \( \gamma=2\beta \) and \( \beta=3\alpha \).
\( \alpha=18^{\circ};\ \beta=54^{\circ};\ \gamma=108^{\circ} \)
\( \alpha=15^{\circ};\ \beta=45^{\circ};\ \gamma=90^{\circ} \)
\( \alpha=12^{\circ};\ \beta=54^{\circ};\ \gamma=111^{\circ} \)
\( \alpha=54^{\circ};\ \beta=18^{\circ};\ \gamma=108^{\circ} \)
1103021704
Level:
A
Decide according to the diagram, which of the line segments \( a \), \( b \), \( c \), \( d \), \( e \) is the longest.
\( d \)
\( a \)
\( b \)
\( c \)
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.
\( 96^{\circ};\ 42^{\circ};\ 42^{\circ} \)
\( 84^{\circ};\ 48^{\circ};\ 48^{\circ} \)
\( 12^{\circ};\ 84^{\circ};\ 84^{\circ} \)
\( 96^{\circ};\ 96^{\circ};\ 12^{\circ} \)
1103021702
Level:
A
Given the triangle \( ABC \) (see the picture), where \( \alpha:\beta=5:7 \) and the angle \( \gamma \) is by \( 42^{\circ} \) smaller than the angle \( \omega \), calculate the measure of \( \gamma \).
\( 108^{\circ} \)
\( 42^{\circ} \)
\( 30^{\circ} \)
\( 60^{\circ} \)