№1
Из теоремы о сумме углов в треугольнике получаем, что третий угол треугольника равен:
1)180*−40*−130*=10*
Тогда внешний угол при третьей вершине равен:
2)180*−10*=170*
Ответ:170*
№2
<span>Угол </span><span><span><span><span><span><span><span><span><span>100*</span></span></span></span></span></span></span></span></span><span> - тупой и поэтому не может быть углом при основании равнобедренного треугольника. Значит, это угол при вершине.</span>
<span><span>Тогда на два угла при основании приходится </span><span><span><span><span><span><span><span><span><span>180*</span></span></span></span><span>−</span><span><span><span><span>100*</span></span></span></span><span>=</span><span><span><span><span>80*</span></span></span></span></span></span></span></span></span><span>. Поэтому угол при основании равен </span><span><span><span><span><span><span><span><span><span>80*</span></span></span></span><span>:</span><span>2</span><span>=</span><span><span><span><span>40*</span></span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span><span>Ответ:40*</span></span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span><span>№3</span></span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span><span><span>Один угол прямоугольного треугольника равен </span><span><span><span><span><span><span><span><span><span>90*</span></span></span></span></span></span></span></span></span><span>, поэтому сумма двух других углов равна </span><span><span><span><span><span><span><span><span><span>180*</span></span></span></span><span>−</span><span><span><span><span>90*</span></span></span></span><span>=</span><span><span><span><span>90*</span></span></span></span><span>.</span></span></span></span></span></span><span> Если один острый угол равен </span><span><span><span><span><span><span><span><span><span>40*</span></span></span></span></span></span></span></span></span><span>, то второй </span><span><span><span><span><span><span><span><span><span>90*</span></span></span></span><span>−</span><span><span><span><span>40*</span></span></span></span><span>=</span><span><span><span><span>50*</span></span></span></span><span>.</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>Тогда внешний угол будет равен </span><span><span><span><span><span><span><span><span><span>180*</span></span></span></span><span>−</span><span><span><span><span>50*</span></span></span></span><span>=</span><span><span><span><span>130*</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>
<span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span><span>Ответ:130*</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>