Question

Кутi DEFi MEF - суміжні , промінь EK - бісектриса кута DEF, кут KEF на 78 градусів менший від кута MEF.Знайдіть куті DEF i MEF

Answer 1

<KEF =<MEF-72°
<DEF=2*KEF = 2MEF-144° (ЕК - биссектриса)
DEF+MEF=180° (смежные)
Итак, 2*<MEF-144°+<MEF =180°
3*MEF=324°
MEF = 108°
DEF= 72 °

Answer 2

Angle Relationships in Triangle DEF

To find the measures of angles DEF and MEF, we can use the given information about the relationship between angle KEF and angle MEF.

Let's break down the given information:

- Angle KEF is 78 degrees smaller than angle MEF. - Angle EK is the bisector of angle DEF.

To find the measures of angles DEF and MEF, we can use the following steps:

1. Let's assume the measure of angle MEF is x degrees. 2. According to the given information, angle KEF is 78 degrees smaller than angle MEF. So, the measure of angle KEF is (x - 78) degrees. 3. Angle EK is the bisector of angle DEF, which means it divides angle DEF into two equal angles. So, the measure of angle DEF is twice the measure of angle EK, which is 2 * (x - 78) degrees.

Therefore, the measures of angles DEF and MEF are as follows:

- Angle DEF: 2 * (x - 78) degrees - Angle MEF: x degrees

Please note that the exact values of angles DEF and MEF cannot be determined without knowing the measure of angle MEF. The given information only provides a relationship between angle KEF and angle MEF.