(a) find x + y + z

(b) find x + y + z + w

Open in App

Solution

(a) x + 90° = 180° (Linear pair)

x = 90°

z + 30° = 180° (Linear pair)

z = 150°

y = 90° + 30° (Exterior angle theorem)

y = 120°

x + y + z = 90° + 120° + 150° = 360°

(b)

Sum of the measures of all interior angles of a quadrilateral is 360º. Therefore, in the given quadrilateral,

a + 60° + 80° + 120° = 360°

a + 260° = 360°

a = 100°

x + 120° = 180° (Linear pair)

x = 60°

y + 80° = 180° (Linear pair)

y = 100°

z + 60° = 180° (Linear pair)

z = 120°

w + 100° = 180° (Linear pair)

w = 80°

Sum of the measures of all interior angles = x + y + z + w

= 60° + 100° + 120° + 80°

= 360°

Suggest Corrections

Similar questions

x = y^{a}, y = z^{b}, z = x^{c}

x, y, z, w

[\begin{matrix} x + y & x - y y + z + w & 2 w - z \end{matrix}] = [\begin{matrix} 2 & - 1 9 & 5 \end{matrix}]

w, x, y, z

w = x = y

z = 2 x

w, x, y, z

x = y^{a}, y = z^{b}

z = x^{c}

a b c

[\begin{matrix} x y & 4 \\ z + 6 & x + y \end{matrix}] = [\begin{matrix} 8 & w \\ 0 & 6 \end{matrix}]

Join BYJU'S Learning Program