Question

1. triangle with angles 93°, 53°, and angle at vertex r (to find). 10) triangle with angles 102°, (x)°, and (2x)° (vertex r at left). handwritten notes: 36, 72 + 180 -77 -77 =34 (partial). worksheet has color sections: yellow, purple, orange, red, pink, yellow (grid layout).

Explanation:

Answer:

1. To find the measure of angle \( R \) in the triangle, we use the fact that the sum of the interior angles of a triangle is \( 180^\circ \). Let \( \angle R = x \). Then:

\( x + 93^\circ + 53^\circ = 180^\circ \)
\( x + 146^\circ = 180^\circ \)
\( x = 180^\circ - 146^\circ = 34^\circ \)

1. For the triangle with angles \( x^\circ \), \( 102^\circ \), and \( 2x^\circ \), we use the angle - sum property of a triangle:

\( x + 102 + 2x=180 \)
\( 3x+102 = 180 \)
\( 3x=180 - 102=78 \)
\( x = 26 \)

So, for problem 6, the measure of angle \( R \) is \( 34^\circ \); for problem 10, \( x = 26 \).