Name: Understanding Different Types of Triangles
Uploaded: 2019-07-19
Duration: 4 min 56 s
Description: The topic of Triangles is the most important in Geometry. In this video, let us learn all about the four types of triangles: right-angled, equilateral, isosceles, and scalene triangles.

Question

Find the sum of all the marked angles in the given figure. $A P Q D, B P S G, C Q R F$ and $H S R E$ are straight lines.

Accepted Answer

The given figure is,

In $△ A P B$ ,

$a + b + ∠ A P B = 180 ° . . . (1)$

In $△ H S G$ ,

$h + g + ∠ H S G = 180 ° . . . (2)$

In $△ F R E$ ,

$f + e + ∠ F R E = 180 ° . . . (3)$

In $△ C Q D$ ,

$c + d + ∠ C Q D = 180 ° . . . (4)$

Now, adding the equations $(1), (2), (3), & (4)$ , we get,

$a + b + ∠ A P B + h + g + ∠ H S G + f + e + ∠ F R E + c + d + ∠ C Q D = 180 ° + 180 ° + 180 ° + 180 °$

$a + b + h + g + f + e + c + d + ∠ C Q D + ∠ A P B + ∠ F R E + ∠ H S G = 720 ° . . . (5)$

Now, $P Q R S$ is a quadrilateral.

Therefore, $∠ S P Q + ∠ P Q R + ∠ Q R S + ∠ R S P = 360 °$

$\Rightarrow ∠ A P B + ∠ C Q D + ∠ E R F + ∠ G S H = 360 °$ ( $∠ S P Q = ∠ A P B, ∠ P Q R = ∠ C Q D, ∠ Q R S = ∠ E R F, ∠ R S P = ∠ G S H$ are vertically opposite angles and are equal)

Now, substituting $∠ A P B + ∠ C Q D + ∠ E R F + ∠ G S H$ value in the equation $(5)$ , we get,

$a + b + h + g + f + e + c + d + 360 ° = 720 °$

$\Rightarrow a + b + h + g + f + e + c + d = 720 ° - 360 ° = 360 °$

Hence, the sum of all the angles is equal to $360 °$ .

Find the sum of all the marked angles in the given figure. $A P Q D, B P S G, C Q R F$ and $H S R E$ are straight lines.

Important Questions on Properties of Triangles

Learn and Prepare for any exam you want !

Find the sum of all the marked angles in the given figure. APQD, BPSG, CQRF and HSRE are straight lines.

Important Questions on Properties of Triangles

Learn and Prepare for any exam you want !

Find the sum of all the marked angles in the given figure. $A P Q D, B P S G, C Q R F$ and $H S R E$ are straight lines.