Question

*The four angles of a quadrilateral are x, x + 5, x-5 and 30 degrees. So what is the measure of the largest angle?*

1️⃣ 120°
2️⃣ 110°
3️⃣ 115°
4️⃣ 105°​

Answer 1

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Step-by-step explanation:

120⁰

Answer 2

Answer:

${ \large{ \pmb{ \sf{Given... }}}}$

Four angles of quadrilateral are x, x + 5, x-5, 30

${ \large{ \pmb{ \sf{To \: Find... }}}}$

Measure of largest angles

${ \large{ \pmb{ \sf{Solution... }}}}$

• We know that, Sum of all angles in any quadrilateral is equal to 360° . Let us add all angles.

${ \implies{ \sf{x + x + 5 + x - 5 + 30 = 360°}}}$

${ \implies{ \sf{3x + 30 = 360°}}}$

$\: { \implies{ \sf{3x = 360° - 30}}}$

$\: { \implies{ \sf{3x = 330°}}}$

$\: { \implies{ \sf{x = 110°}}}$

${ \large{ \pmb{ \sf{Finding \: All \: Angles... }}}}$

$: \: \: \to \: \sf{First \: Angle = x = 110°}$

${ : \: \: {\to {\sf{second \: angle = x + 5 = 110 + 5 = 115°}}}}$

${ : \: \: {\to {\sf{Third Angle =x - 5 = 110 - 5 = 105 °}}}}$

${ : \: \: { \to{ \sf{Fourth \: Angle = 30°}}}}$

${ \large{ \pmb{ \sf{ Final \: Answer... \: }}}}$

The largest angle = 115°

Therefore,

• Option 3 is your answer