Find Unknown Angle

This is a rhombus. Find the measure for ∠H:

• H= 180 degrees

• H= 65 degrees

• H= 115 degrees

This is a trapezoid. Find the measure of ∠K:

• 114°

• 124°

• 77°

• 66°

Calculate, in degrees, the size of the marked unknown angle.

Give your answer correct to 1 decimal place.

Answer explanation

$Sin\left(x\right)\ =\ \frac{Opp}{Hyp}$

$\sin\left(x\right)\ =\ \frac{5.5}{6}$

$x\ =\ \sin^{-1}\left(\frac{5.5}{6}\right)$


$x\ =66.44353569$

$x\ =\ 66.4\degree\ \left(1\ dp\right)$

Calculate, in degrees, the size of the marked unknown angle.

Answer explanation

 $Sin\left(x\right)\ =\ \frac{Opp}{Hyp}$  

 $\sin\left(x\right)\ =\ \frac{3}{6}$  

 $x\ =\ \sin^{-1}\left(\frac{3}{6}\right)$  


 $x\ =\ 30\degree$  

Calculate, in degrees, the size of the marked unknown angle.
Give your answer correct to 1 decimal place.

Answer explanation

 $Sin\left(x\right)\ =\ \frac{Opp}{Hyp}$  

 $\sin\left(x\right)\ =\ \frac{8}{14}$  

 $x\ =\ \sin^{-1}\left(\frac{8}{14}\right)$  


 $x\ =\ 34.84990458$  

 $x\ =\ 34.8\degree\ \left(1\ dp\right)$   

Calculate, in degrees, the size of the marked unknown angle.

Give your answer correct to 1 decimal place.

Answer explanation

$Sin\left(x\right)\ =\ \frac{Opp}{Hyp}$

$\sin\left(x\right)\ =\ \frac{10}{11}$

$x\ =\ \sin^{-1}\left(\frac{10}{11}\right)$


$x\ =65.38002267$

$x\ =\ 65.4\degree\ \left(1\ dp\right)$

Calculate, in degrees, the size of the marked unknown angle.

Give your answer correct to 1 decimal place.

Answer explanation

$Sin\left(x\right)\ =\ \frac{Opp}{Hyp}$

$\sin\left(x\right)\ =\ \frac{7}{12}$

$x\ =\ \sin^{-1}\left(\frac{7}{12}\right)$


$x\ =35.68533471$

$x\ =\ 35.7\degree\ \left(1\ dp\right)$

Calculate, in degrees, the size of the marked unknown angle.

Give your answer correct to 1 decimal place.

Answer explanation

$Sin\left(x\right)\ =\ \frac{Opp}{Hyp}$

$\sin\left(x\right)\ =\ \frac{6}{9}$

$x\ =\ \sin^{-1}\left(\frac{6}{9}\right)$


$x\ =41.8103149$

$x\ =\ 41.8\degree\ \left(1\ dp\right)$

Calculate, in degrees, the size of the marked unknown angle.

Give your answer correct to 1 decimal place.

Answer explanation

$Sin\left(x\right)\ =\ \frac{Opp}{Hyp}$

$\sin\left(x\right)\ =\ \frac{4}{11}$

$x\ =\ \sin^{-1}\left(\frac{4}{11}\right)$


$x\ =21.32368626$

$x\ =\ 21.3\degree\ \left(1\ dp\right)$

Calculate, in degrees, the size of the marked unknown angle.

Give your answer correct to 1 decimal place.

Answer explanation

$Sin\left(x\right)\ =\ \frac{Opp}{Hyp}$

$\sin\left(x\right)\ =\ \frac{3}{12}$

$x\ =\ \sin^{-1}\left(\frac{3}{12}\right)$


$x\ =14.47751219$

$x\ =\ 14.5\degree\ \left(1\ dp\right)$