Question

ABCD параллелограмм ВЕ биссектриса угла С Угол ВЕА 62° Найти углы параллелограмма

Answer 1

Условие: ABCD параллелограмма, ВЕ биссектриса угла АВС, угол ВЕА 62°. Найти углы параллелограмма.

Решение: Угол ВЕА=углу СВЕ как накрест лежащие при параллельных АD и ВС и секущей ВЕ. ВЕ биссектриса, значит <B параллелограмма равен 2*62=124 градуса. Углы, прилежащие к одной стороне в сумме равны 180. Тогда угол А=180-124=56 градусов. <A=56, <B=124, <C=56 и <D=124

Answer 2

Given Information:

We are given that ABCD is a parallelogram, and VE is the bisector of angle C. We are also given that angle VEA measures 62°. We need to find the measures of the angles of the parallelogram.

Solution:

To find the measures of the angles of the parallelogram, we can use the properties of parallelograms.

1. Opposite angles in a parallelogram are congruent. Therefore, angle A is congruent to angle C, and angle B is congruent to angle D.

2. The sum of the measures of adjacent angles in a parallelogram is 180°. Therefore, angle A + angle B = 180°, and angle C + angle D = 180°.

Based on these properties, we can find the measures of the angles of the parallelogram.

Let's denote angle A as x. Since angle A is congruent to angle C, we can say that angle C is also x.

Using the property that the sum of adjacent angles is 180°, we can write the equation:

x + angle B = 180°

Since angle B is congruent to angle D, we can rewrite the equation as:

x + x = 180°

Simplifying the equation, we get:

2x = 180°

Dividing both sides of the equation by 2, we find:

x = 90°

Therefore, angle A = angle C = 90°.

Since opposite angles in a parallelogram are congruent, we can conclude that angle B = angle D = 90°.

So, the measures of the angles of the parallelogram ABCD are:

Angle A = Angle C = 90°

Angle B = Angle D = 90°