Question

if these two figures are similar, what is the measure of the missing angle? 87° 59° 34° ?

Explanation:

Step1: Recall angle - sum property of triangles

The sum of interior angles of a triangle is 180°.

Step2: Use similarity of triangles

Similar triangles have equal corresponding angles. Let the missing angle be $x$. For the first triangle, the sum of its angles is $87^{\circ}+59^{\circ}+34^{\circ}=180^{\circ}$. Since the two triangles are similar, the missing angle in the second triangle has the same measure as one of the angles in the first triangle.

Step3: Determine the missing - angle value

The missing angle $x$ is equal to one of the angles of the first triangle. We can find it using the angle - sum property. Let's assume the missing angle corresponds to the $34^{\circ}$ angle (it could be any of the non - given angles in the second triangle based on similarity). So $x = 34^{\circ}$.

Answer:

$34$