Question

4.
In a triangle, the sum of two angles is equal to
the third angle, if the difference between two
angles is 30°, the angles are
(1) 15°, 45°, 75° (2) 20°, 50°, 80°
(3) 30°, 60°, 90° (4) 45°, 45°, 90°
If the given system of equations has infinite​

Answer 1

$\huge\bold\green{answer- }$

$\star\fbox\blue{given - }$

$\pink{ \star \: difference \: of \: two \:angles \: = 30 \degree }$

$\star\fbox\blue{find- }$

$\pink{\star \: all \: the \: angles \: of \: a \: \triangle}$

$\huge\tt\underline \red{solution- }$

$\blacktriangleright \: as \: we \: know \: that \: - \\ \purple{ \leadsto \: sum \: of \: all \: the \: \angle \: es \: of \: a \: \triangle = 180 \degree}$

$\longmapsto \angle \: a \: + \angle \: b \: = \angle \: c \:$

$\longmapsto \angle \: a \: - \angle \: b \: = 30 \degree$

$2c = 180 \degree \\ \\ c = \frac{180}{2} \\ \\ = 90 \degree$

$\longmapsto\angle \: a - \angle \: b = 30 \degree$

$\longmapsto \angle \: a + \angle \: b \: = \angle \: 90 \degree$

$2a = \frac{120}{2} \\ \\ a = 60 \degree$

$\angle \: b \: =180 \degree - ( 90 \degree + 60 \degree )\\ =180 \degree - 150 \degree \\ = 30 \degree$

$\therefore \\ \red{\hookrightarrow \angle \: a = 60 \degree} \\ \red{\hookrightarrow \angle \: b = 30 \degree} \\\red{ \hookrightarrow \angle \: c \: = 90 \degree}$

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