Answer: The required measure of the indicated angle is 31°.
Step-by-step explanation: We are given to find the measure of the indicated angle in the figure.
Let the measure of the indicated angle be x°.
From the figure, we see that there are two triangles. The measures of the two angles of one triangle are 52° and 49°.
And, the measure of one of the angles of the second triangle is 70°.
The third angle of both the triangles are vertically opposite to each other, so they must be equal.
Since the sum of the three angles of any triangle is 180°, so we must have
[tex]52^\circ+49^\circ=70^\circ+x^\circ\\\\\Rightarrow 52+49=70+x\\\\\Rightarrow 101=70+x\\\\\Rightarrow x=101-70\\\\\Rightarrow x=31.[/tex]
Thus, the required measure of the indicated angle is 31°.
