Question

ABCD is a quadrilateral with angle A and angle B respectively. If angle C=60° and angle D=40° find the angle APB.​

Answer 1

$\textbf{\huge{ANSWER:}}$

Given:

Angle C = 100°

Angle D = 50°

ABCD is a quad.

To find:

Angle APB

Solution:

In quad ABCD = Angle ( A + B + C + D ) = 360° [ Angles of a quad = 360° ]

=》 360° = 100° + 50° + Angle ( A + B )

=》 360° - 150° = Angle ( A + B )

=》 210° = Angle A + Angle B ...(1)

In Triangle APB:

$\begin{gathered}\frac{1}{2}\\\end{gathered} </p><p>$

(A + B) + Angle P = 180° [ Angle Sum Property ] ...(2)

=》 Due to (1), we have Angle A + Angle B = 210°

$\begin{gathered}\frac{1}{2}\\\end{gathered}$

(A + B) =

$\begin{gathered}\frac{210}{2}\\\end{gathered} </strong></p><p><strong>[tex]\begin{gathered}\frac{210}{2}\\\end{gathered}$

$=》 \begin{gathered}\frac{1}{2}\\\end{gathered} </p><p>$

(A + B) = 105° ....(3)

(3) in (2):

=》 180° = 105° + Angle P

$=》 \textbf{75° = Angle P}75° </p><p>$

Hope it Helps!! :)