Triangles

1103076905

Level: 
A
The triangle in the diagram is divided into two isosceles triangles \( AKC \) and \( KBC \) which have the same area. Calculate the size of the angle \( \beta \) if you know that the measure of \(\measuredangle AKC \) is \( 140^{\circ} \).
\( 70^{\circ} \)
\( 60^{\circ} \)
\( 50^{\circ} \)
\( 40^{\circ} \)

2000003202

Level: 
A
An isosceles triangle \(ABC\) is given in the picture. What are the measures of its interior angles?
\( \alpha=27^{\circ};~\beta=27^{\circ};~\gamma=126^{\circ}\)
\( \alpha=54^{\circ};~\beta=54^{\circ};~\gamma=72^{\circ}\)
\( \alpha=63^{\circ};~\beta=63^{\circ};~\gamma=153^{\circ}\)
\( \alpha=126^{\circ};~\beta=27^{\circ};~\gamma=27^{\circ}\)

2000003203

Level: 
A
A deltoid is composed of two isosceles triangles that have a common base. See the picture. Find the measures of the deltoids interior angles.
\( \alpha=36^{\circ};~\beta=134^{\circ};~\gamma=56^{\circ};~\delta=134^{\circ}\)
\( \alpha=36^{\circ};~\beta=100^{\circ};~\gamma=56^{\circ};~\delta=100^{\circ}\)
\( \alpha=56^{\circ};~\beta=134^{\circ};~\gamma=56^{\circ};~\delta=134^{\circ}\)
\( \alpha=36^{\circ};~\beta=128^{\circ};~\gamma=56^{\circ};~\delta=128^{\circ}\)

2010015201

Level: 
A
Interior angles of a triangle \( ABC \) are in the ratio \( \alpha:\beta:\gamma=3:5:7 \). Calculate the measures of these angles.
\( \alpha=36^{\circ};\ \beta=60^{\circ};\ \gamma=84^{\circ} \)
\( \alpha=30^{\circ};\ \beta=50^{\circ};\ \gamma=70^{\circ} \)
\( \alpha=16.5^{\circ};\ \beta=30^{\circ};\ \gamma=133.5^{\circ} \)
\( \alpha=84^{\circ};\ \beta=60^{\circ};\ \gamma=36^{\circ} \)