# Finding the Value of Angle $x$ in a Concave Quadrilateral

**URL:** <https://sorumatik.co/t/finding-the-value-of-angle-x-in-a-concave-quadrilateral/667082>\
**Category:** Maths Question\
**Created:** [Haziran 25, 2026, 9:32öö UTC](https://sorumatik.co/t/finding-the-value-of-angle-x-in-a-concave-quadrilateral/667082 "2026-06-25T09:32:11Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Kaanburak](https://sorumatik.co/user_avatar/sorumatik.co/kaanburak/32/59364_2.png) [@Kaanburak](https://sorumatik.co/u/Kaanburak)\
**Post date:** [Haziran 25, 2026, 9:32öö UTC](https://sorumatik.co/t/finding-the-value-of-angle-x-in-a-concave-quadrilateral/667082/1 "2026-06-25T09:32:12Z")

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Don t Use Pen and raper  
50°  
110°  
C=?

 ![Soru Görseli](https://sorumatik.co/uploads/default/original/3X/0/6/06fe187927c47ef7cfc96312eeb8f840e9cec83d.jpeg)

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**Author:** ![Egitim\_Danismani](https://sorumatik.co/user_avatar/sorumatik.co/egitim_danismani/32/86791_2.png) [@Egitim\_Danismani](https://sorumatik.co/u/Egitim_Danismani)\
**Post date:** [Haziran 25, 2026, 9:32öö UTC](https://sorumatik.co/t/finding-the-value-of-angle-x-in-a-concave-quadrilateral/667082/2 "2026-06-25T09:32:17Z")

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## Finding the Value of Angle x in a Concave Quadrilateral

💡 **[RULE / FORMULA USED:]** **The Exterior Angle Property of a Concave Quadrilateral (Arrowhead Property)** states that the interior reflex angle (or the interior non-reflex angle pointing outward) is equal to the sum of the three interior opposite angles.  
Formula: \text{Angle } C = \text{Angle } A + \text{Angle } B + \text{Angle } D

🧠 **[SOLUTION STEPS:]**

**Step 1 — Identify the Given Values**  
In the provided image, we have a concave quadrilateral ABCD. The internal angles given are:

- Angle B = 50^\circ
- Angle D = 50^\circ
- The interior angle at C = 110^\circ
- The angle at A = x

**Step 2 — Apply the Arrowhead Theorem**  
According to the geometric property of this shape, the angle located at the “indent” (Angle C) is the sum of the three pointed angles (A, B, and D).  
Equation: 110^\circ = x + 50^\circ + 50^\circ

**Step 3 — Simplify and Solve for x**  
First, add the known angles on the right side:  
50^\circ + 50^\circ = 100^\circ  
Now, the equation is:  
110^\circ = x + 100^\circ

Subtract 100^\circ from both sides to isolate x:  
x = 110^\circ - 100^\circ  
x = 10^\circ

━━━━━━━━━━━━━━━━━━━━━━━━━━━  
✅ **[ANSWER:]** x = 10^\circ  
━━━━━━━━━━━━━━━━━━━━━━━━━━━

🎯 **[KEY CONCEPTS:]**

**1. Concave Quadrilateral (Arrowhead)**

- **[Definition:]** A quadrilateral where one interior angle is greater than 180^\circ (reflex angle).
- **[In this problem:]** The shape ABCD forms an arrowhead where the exterior-facing angle at C is the sum of the other three.

**2. Sum of Interior Angles**

- **[Definition:]** The sum of interior angles of any quadrilateral is always 360^\circ.
- **[In this problem:]** If you consider the reflex angle at C (360^\circ - 110^\circ = 250^\circ), then x + 50^\circ + 50^\circ + 250^\circ = 360^\circ, which also results in x = 10^\circ.

⚠ **[COMMON MISTAKES:]**

**❌ Incorrect Shape Identification**

- **[Wrong:]** Treating the shape as a standard triangle and assuming x + 50 + 50 = 180.
- **[Right:]** Recognizing this is a four-sided concave polygon, not a simple triangle.
- **[Why it’s wrong:]** There are four vertices (A, B, C, D), making it a quadrilateral governed by different angle properties.

Would you like me to explain how to prove the Arrowhead Theorem using auxiliary lines?