Find missing angles (straight line, corner, crossing lines)
Grade 7 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.
Kira draws a line out from the square corner of an envelope for a secret-club stamp. It splits the corner into complementary angles, 28° and (4x + 10)°. What is x?
Milo's scissor blades cross like an X. The (4x + 12)° and 112° angles are vertical angles, across from each other. What is x?
Labeled sketch, not to scale: two straight lines cross at one point. The angle marked (4x + 12)° is across from the angle marked 112°. Labeled sketch, not to scale: two straight lines cross at one point. The angle marked (4x + 12)° is across from the angle marked 112°. 112° (4x + 12)° Not to scale. Ren cuts a pizza with three straight cuts through the middle, making six slices. Two angles are marked 52° and 67°, as the sketch shows. What is angle x, in degrees?
Labeled sketch, not to scale: three straight lines cross at one point, making six angles. Going around the point in order: 52°, an empty angle, x°, an empty angle, 67°, an empty angle. Labeled sketch, not to scale: three straight lines cross at one point, making six angles. Going around the point in order: 52°, an empty angle, x°, an empty angle, 67°, an empty angle. 52° x° 67° Not to scale. Ari opens the music room door against a straight wall. The angles on each side of the door are (2x)° and (3x + 20)°. How big is the (3x + 20)° angle, in degrees?
Labeled sketch, not to scale: a straight line with one ray from a point on it. The two angles side by side are marked (2x)° and (3x + 20)°. Labeled sketch, not to scale: a straight line with one ray from a point on it. The two angles side by side are marked (2x)° and (3x + 20)°. (2x)° (3x + 20)° Not to scale. Esme draws a line out from the square corner of a poster. It splits the corner into (2x)° and (3x + 5)°. How big is the (3x + 5)° angle, in degrees?
Labeled sketch, not to scale: a square corner with its right-angle mark, split by one ray into two angles marked (2x)° and (3x + 5)°. Labeled sketch, not to scale: a square corner with its right-angle mark, split by one ray into two angles marked (2x)° and (3x + 5)°. Labeled sketch, not to scale (2x)° (3x + 5)° Jun tapes a paper snowflake chain out from the square corner of a window. It splits the corner into (4x)° and (2x + 6)°. How big is the (2x + 6)° angle, in degrees?
Labeled sketch, not to scale: a square corner with its right-angle mark, split by one ray into two angles marked (4x)° and (2x + 6)°. Labeled sketch, not to scale: a square corner with its right-angle mark, split by one ray into two angles marked (4x)° and (2x + 6)°. (4x)° (2x + 6)° Not to scale. Kira sets an open book flat, and two pages stand up from the spine. Along the covers the angles are 35°, (3x)° and 64°. Which equation finds x?
Labeled sketch, not to scale: a straight line with two rays from one point on it, making three angles side by side: 35°, (3x)° and 64°. Labeled sketch, not to scale: a straight line with two rays from one point on it, making three angles side by side: 35°, (3x)° and 64°. 35° (3x)° 64° Not to scale. - 3x = 35 + 64
- 35 + 3x + 64 = 180
- 35 + 3x + 64 = 90
- 35 + 3x + 64 = 360
Milo stitches two lines out from the square corner of a quilt square. They split the corner into 21°, (2x)° and 37°. Which equation finds x?
Labeled sketch, not to scale: a square corner with its right-angle mark, split by two rays into three angles side by side: 21°, (2x)° and 37°. Labeled sketch, not to scale: a square corner with its right-angle mark, split by two rays into three angles side by side: 21°, (2x)° and 37°. 21° (2x)° 37° Not to scale. - 2x = 21 + 37
- 21 + 2x + 37 = 90
- 21 + 2x + 37 = 180
- 21 + 2x + 37 = 360
Noah cuts two lines out from the square corner of a paper square for a pinwheel. They split the corner into 26°, (x + 5)° and 33°. Which equation finds x?
Labeled sketch, not to scale: a square corner with its right-angle mark, split by two rays into three angles side by side: 26°, (x + 5)° and 33°. Labeled sketch, not to scale: a square corner with its right-angle mark, split by two rays into three angles side by side: 26°, (x + 5)° and 33°. Labeled sketch, not to scale 26° (x + 5)° 33° - 26 + x + 5 + 33 = 90
- x + 5 = 26 + 33
- 26 + x + 5 + 33 = 360
- 26 + x + 5 + 33 = 180
Ari's toy sailboat has a triangle sail. The sail's angles are (2x)°, (2x + 6)° and 74°. What is x?
Labeled sketch, not to scale: a triangle with its three angles marked (2x)°, (2x + 6)° and 74°. Labeled sketch, not to scale: a triangle with its three angles marked (2x)°, (2x + 6)° and 74°. (2x)° (2x + 6)° 74° Not to scale